yes, candlemas day is currently close to a cross -quarter day in the irish calendar..(birth of spring)

but birth of spring is holiday about spring (new beginnings, and blessings on new year) and about lambing.. (lambs start giving birth in the month of February) no doubt, goats do too. so lambs and goats, and beginnings, and blessing --there is a good deal of overlapping of pagan ideas of the roman and the irish.

maybe candlemas day used to be the same day as dies februare, and got moved to Feb 2, to move it closer to the irish calendar holiday (which is somewhat similar in nature) --that is just a WAG on my part..
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WW--if you venture to this thread, you might not like the info in the rest of this post.. (guessing from your stated feelings about chickens and pigs)
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ewes that have their lambs still born, can behave in a way similar to, what in humans, is called mourning. they don't recover from the birth, become ill, and can die.

and lambs that are born orphans, or rejected, as sometimes happens, by their mother, will starve to death.

one common solution is for the shepherds to take the still born lamb, and skin it. then to place the skin over the head and back of the orphan, (so it 'smells right' to the mother.) a mother will accept an lamb dressed up in her lambs 'skin' as her own, most of the time.

so part of normal lambing involves skinning some lambs.