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By Petting, and talking to, and hand-feeding, your hourse.
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.
You feed it Fodder.
1.Hand feeding it 2.Brushing it 3.Talking to it Its very easy
You have to take it outside, then go next to it and click 'Z' on the Wii Nunchuk and you will climb on it
Unlike the Harvest Moon Game for Gamecube you can not make your Horse Jump.
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