You still can. When you stand next to your horse, press CTRL and you see the ring menu come up. Then click on the heart icon that says "Commune". This allows you to restore some stamina to the horse, but it has a cooldown (and the stam recovered is very low).

My particular horse doesn't have the F9 option. I'm guessing because it was a lower tier that was converted into a T6? 

Thank you for answering. 

Huh thats weird, do you have a screenshot?