How do you give your horse a companion on Howrse?

The dog is a companion for your horses. When they play together, it'll give you all kinds of advantages:

Dressage bonus: +15

Until 18 months:

A gain in Genetic Potential for each hour of play

From 20 months until 25 years old:

Earning per hour of play: 0.15 skills (limited to 60 per horse)