In a lot of lore about spirits, you tend to find that offerings are very much encouraged when trying to build a relationship with them, but too much gratitude will backfire spectacularly. The gruagach is helpful so long as they are treated right; it is traditional to leave some milk for them in the hollow of a special stone, with offerings given to them at Bealltainn as well, and in some places the offerings are kept up (though unfortunately the one video I've seen about it has now been taken down). Traditionally, if their offerings are neglected the gruagach might not look after your cattle, or worse - they might deliberately lead them to harm. In many ways, the gruagach bears all the hallmarks of a pre-Christian local deity, even if their name might not be known anymore, but according to some the gruagach may be a ghost of someone local, who haunts the glens and looks kindly on people.
Thomas Pennant and Martin Martin both write about the gruagach in their work dating back to the late seventeenth and eighteenth centuries, and you can find an essay on the gruagach in one of Pennant's volumes. Their name refers to their long hair (a motif that points to their Otherworldly nature), and usually they're female. In some parts of Scotland, like on Skye, they're more likely to be male (and tend to be the default explanation for how a pretty young maid might have got pregnant out of wedlock while she was up on the summer pastures).
So in general, they seem to be the kind of spirits that we want to propitiate, and it all seems quite simple. Looking through the Carmina Gadelica late one night last week, though, I found some interesting notes on the gruagach in Volume II, which have coincidentally good timing for Samhainn:
Gruagach, a supernatural female who presided over cattle and took a kindly interest in all that pertained to them. In return a libation of milk was made to her when the women milked the cows in the evening. If the oblation were neglected, the cattle, notwithstanding all precautions, were found broken loose and in the corn; and if still omitted, the best cow in the fold was found dead in the morning. The offering was poured on 'clach na gruagaich,' the 'gruagach' stone. There is hardly a district in the Highlands which does not possess a 'leac gruagaich'--a 'gruagach,' flag-stone--whereon the milk libation was poured. I have seen such stones in Arran, Kintyre, Gigha, Islay, Mull, Lismore, Kerara, Lorn, Iona, Tiree, Coll, Barra, South Uist, Benbecula, North Uist, Heisgeir, St Kilda, Harris, Lewis, Sutherland, Ross, at Culloden, Cawdor, Lochaber, and in various other places. All these oblation stones are erratic ice-blocks. Some of them have a slight cavity into which the milk was poured; others have none, the libation being simply poured on the stone. In making the oblation the woman intoned a rune--
'A ghruagach, a ghruagach,
Cum suas mo spreidhe,
Cum sios an Guaigean,
Cum uap an Geige.'
Uphold my herds,
Keep down the 'Guaigean,'
Keep from them the 'Geige.'
There is probably no district in the Highlands where the 'gruagach' could not be fully described. A woman living in the remote island of Heisgeir described her so graphically and picturesquely that her interested listener could almost see moving about in the silvery light of the kindly moon the 'gruagach' with her tall conical hat, her rich golden hair falling about her like a mantle of shimmering gold, while with a slight swish of her wand she gracefully turned on her heel to admonish an unseen cow. At intervals he seemed to hear her mellow voice in snatches of eerie song as she moved about among the grassy ruins of the old nunnery--all silent now of the holy orisons of gentle sisters.
The thing that interested me the most was the mention of the 'Guaigean' and the 'Geige' - it's not something I've seen much about in Scottish lore in general. In another note from Carmichael (at the same link, as above), there is a description of the Geigean:
Geigean, Righ Geigean, Geigean, King Geigean. This was the term applied to the man who presided over the death revels. These were held in winter. Lots were cast, and the man upon whom the lot fell was elected king of the revels, over which he reigned from midnight till the old cock crew. A tub of cold water was poured over his head and down his throat, after which his face and neck were smeared with soot. When the man had been made as formidable and hideous as possible, a sword, scythe, or sickle was placed in his hand as an emblem of office...So the immediate conclusion seems to be that the offerings to the gruagach are in the hopes that the gruagach will then protect people against the Geige (or Géige, as it should be - Carmichael was terrible for not bothering with accents in the first two volumes especially) and the Guaigean. Considering Carmichael's comments on the Righ Geigean we might suspect that the latter perhaps represent spectres of wintry danger or death, effectively. And/or, considering one of the tales in the first link, of the ghostly gruagach who protected against murrain, she works against sickness spreading.
A rhyme common among boys at play says:--
'Thaine mi o chri-chas,
Thaine mi o chruai-chas,
Thaine mi o Ghigean,
Thaine mi o Ghuaigean,
’S thig mi uat-s’ ma dh’f haodas mi.
I came from small peril,
I came from great peril,
I came from Geigean,
I came from Guaigean,
And I will come from thee if I can.
'Gigean' and 'Guaigean' are probably forms of 'Geigean.'
My first thought was to wonder if the rite described might have something to do with Samhainn (since the festival marks the start of winter); Carmichael was notoriously leery of mentioning Samhainn at all, albeit for a brief entry in the notes in volume II and a few other passing mentions, so he's unlikely to spell it out and it wouldn't be any wonder that he was vague on that point. Pulling out my trusty copy of The Gaelic Otherworld, Ronald Black's notes refers to the Righ Geigean ritual as being performed, specifically, at the beginning of winter (see p457), so that seems to confirm it. It's interesting that the taking of lots seems to mirror a similar practice from Bealltainn, where the men would come together and take turns, blindfolded, to pick out piece of bannock from a basket or cloth. In this case, at Bealltainn, whoever got the burnt piece of bannock called the cailleach beal-tine would effectively take on the burden of failure in the coming season; it would be assumed that they would struggle, in order to allow the rest of the community to prosper. It seems a similar idea is intended for the Righ Geigean - they suffer, so others don't have to.
It's not the only instance of Samhainn practices echoing those found at Bealltainn; it seems the practice of making offerings - by throwing pieces of bannock over the shoulder, with a prayer said - to keep away threats from livestock and family was performed at both Bealltainn and Samhainn. Interestingly, according to Dwelly, a guaigean can be defined as either "a thick, little round cake," or else "a short, stout man or boy." A géige, on the other hand, is primarily a branch or sapling, but can also refer to "a young, superfine female, nymph."
I've not found much else on the Géigean, aside from some hints that it may have been related to the urisk (or ùraisg) who often get lumped in with the brownie and gruagach as a kind of helpful spirit. This is a little confusing, because the ùraisg seems to have something of a more mischievous reputation than the others, but is generally harmless and solitary, preferring to hang around waterfalls or streams. If they happen to live near a farm they might also help out around the farmstead if given milk or cream. So not much like the dangers hinted at in Carmichael's prayer. They tended to have a wilder appearance than the gruagach, though, sometimes being described as half-goat, half-man or quite frightening to those who could see them. According to John Gregorson Campbell, at least some of them did have some association with wintry elements:
"A man passing through Srath Dubh-Uisg (near Loch Sloy at the head of Loch Lomond) on a keen frosty night heard an urisk on one side of the glen calling out: Reoth, reoth, reoth. "Frost, frost, frost."
This was answered by another urisk calling from the other side of the glen: Ceige-reoth, ceige-reoth, ceige-reoth. "Kick-frost, kick-frost, kick-frost."
The man, on hearing this, said, "Whether I wait or not for frost, I will never while I live wait for kick-frost." And he ran at his utmost speed till he was out of the glen."
Black, The Gaelic Otherworld, 2005, p106.
Ronald Black's notes on this say that Reoth and Ceige-Reoth more than likely refer to the names of the two urisks in the glen - Frost and Jack Frost, "as it were" (op. cit. p363). Furthermore, Ceige-Reoth here refers to the Géigean, ceige meaning "a mass of matted hair" and - aside from Ceige and Geige being very similar - the word denotes the "wild figure" of the Géigean himself.
All things considered, confusing though it might all be, it offers some food for thought for the coming season.
See also here, if anything, in case you're wondering how to pronounce guaigean!