In order to obtain a horse you must live the dog, befried Chen and Charlie (sometimes it's just Chen) to I believe at least two hearts. Just do the exact the same thig with them as you would do if you were attempting to get the dog. Talk to them everyday until your allowed to give them gifts, then give them stuff that is listen below:

Chen
Likes: Buckwheat,Rice Cake,Boiled egg,Tofu,omlet
Really likes: Natto,corn soup,egg soup,soy milk
Best Gift: Noodles

Charlie
Likes: peach,apple,grape,mixed juice
Strongly likes: Curry bread,Curry Bun,Curry Rice
Best Gift: Dry Curry
Best Gift: Noodles

please keep in mind that you can only give chen gifts on hi days off which is only friday. You can give Charlie stuff when he isn't by the counter.