On Howrse how do you increase your horse's skills?

Ride, train, compete, and do lessons with your Howrse. You can use the water of youth BM item to double the number of lessons he can do, and pieces of cloud to send him back in time 4 months and do extra lessons.

you add skill to your Howrse by doing all the rides, training and playing with companions until you can't any more, the training will go up on a scroll button thing and so will the rides so you know when you have completed them and you will only loose energy with the companion when you have done all the games you can.