Would I be able to open up a service of physically drawing pictures for people's horses, instead of digitally? 

Here's a couple of examples

http://fc09.deviantart.net/fs70/i/2014/003/7/9/quarter_horse_mare_by_mamtebpf-d70nyoi.jpg

http://fc06.deviantart.net/fs71/i/2014/003/3/6/bernese_mountain_dog_by_mamtebpf-d70nztr.jpg

Both were done by me

Yes! :).