Shulchan Arukh, Orach Chayim 523/שולחן ערוך·אורח חיים תקכ״ג

11. Laws regarding animals on the holiday, 4 Seifim: We remove flies that are stuck on an animal, even though this creates a wound.

22. We do not comb an animal with a fine comb on a holiday because this removes hair.

33. We do not deliver an animal on a holiday, but we assist it by holding the newborn such that it does not fall on the ground, blowing in its nose, and putting the teat into its mouth.

44. If an animal spurns its newborn, it is permitted to sprinkle (meaning to pour) the water of the after-birth on it and put salt in her womb so that she will have mercy on it. It is forbidden to do this for an impure animal. Rem"a: (And see above chapter 246 paragraph 3 in the Rem"a's note regarding whether a man is commanded to let his animal rest on a holiday).