Shulchan Arukh, Orach Chayim 536/שולחן ערוך·אורח חיים תקל״ו

1All Animal Needs Can Be Done on Chol Hamoed, 4 Seifim: One who needs to ride on an animal to travel for pleasure or for a holliday need and cannot walk is permitted to trim the horse's hoofs, to fix its horseshoes, saddle, and bridle, and to do any other activity necessary for riding. This assumes that one did not plan to do this work on the holiday. Rema: It is permitted to ride on Chol Hamoed even from city to city and even for no reason, and this is the practice. However, it is prohibited to do activities necessary for riding if one rides neither for a holiday need nor for travel for pleasure (Beit Yosef).

2It is permitted to brush a horse to make it prettier.

3We do not breed animals on the holiday, but we do draw blood. We do not withhold anything medical, even if it involves labor.

4We do not sit a hen on eggs to grow chicks. If she was placed before the holiday and ran away, one can return her (but it is forbidden to put a different one there, even if the first one died) (Beit Yosef). This is only the case when it is within three days of her running away.