Unlike the Harvest Moon Game for Gamecube you can not make your Horse Jump.
You feed it Fodder.
You push it into the barn yourself~
Ride it around town a lot.
You can have Horse, Sheep, and cow
you buy one at the blue sky ranch
stand next to it and press Y
Once you build a Barn you can just buy a Horse from Blue Sky Ranch.
By Petting, and talking to, and hand-feeding, your hourse.
You have to buy them from the place where you can buy animals. Hope this helps. :)
Sorry the only color of horse you can get is brown. But I like Blue's and Alex's Horses
Yes you can you just need to have 2-3 hearts with your horse first.
Hand feed and Brush your horse everyday. If you want you can let your horse outside when the weather is Sunny.