Rename the file to 'horse.xnb' and replace the file in Stardew Valley/Content/Animals.

I recommend backing up the original 'horse.xnb' in case you'd like to ride a horse again.

I used the bear sprites already present in the game and made a few alterations to make the bear ride-able. Not 100% perfect but if you'd like to make adjustments feel free to.

Thanks!