What I expected.
1. I use wheat or some other appropriate food that they are attracted to.
2. I right click them to have them enter 'love mode' and mate.

What actually happened:
I tried various foods and none of them attracted the horses (like wheat would for example) and all right clicking does is mount the horses.

I checked with a cow and it works fine for other mobs.

It's possible that Mojang hasn't implemented breeding for them yet.

Edit: Did a bit more testing and checked in survival mode and although they'll consume some foods, the result is the same.