We compost the pine shavings and straw from the chicken coop, whatever green waste from the kitchen, wood junk from splitting ect. Takes a long time for it to start to break down, but turns out some nice compost. I used some horse manure the other year from a neighbor, but I'll likely get cow manure this spring off my cousin. We're slowly getting the nasty red clay broken up into some nice black dirt. Chicken have been the biggest help. The scratch and poop all over.There are some factors that have not been brought up. What do horses eat? Of course primarily grass during the growing season and hay on the off season. Many horse owners are picky about the hay they feed but no matter how picky they are hay still contains some grass and weed seed. Horses are not great digesters and the manure will contain weed seed. Manure from cattle that are fed hay is even worse. They will both work but you may have greater weed pressure.
Hog and poultry manure is higher in nutrient value per pound and does not have weed seed issues.