In the FAQ it says there are certain limits to the amount of horses a stable can own, but some stable seem to have considerably more… So do the limits actually apply?
Technically there’s a limit of 500 racehorses and 50 stallions (no limit on the other horses), but 1) it’s not enforced 2) I don’t think anyone’s near either limit. 
Sweet… no need to think about my purchases too hard then 
but trying to manage 500 racehorses, what a nightmare!