On Howrse, How Do You Make Your Horses Moral Go Up?

You can increase it's morale by:
Feeding it apples, turnips, carrots, or a salt lick, all for +1 morale
full grooming for +3 morale,
or covering it (stallion or mare) for +10 morale

i hope this helps you!
PS make sure not to put it in it's box, it decreases it's morale.

Feeding it something it likes: Apples, turnips,etc,grooming it, or putting something on it such as a stallion

You can also feed it Caloric Mash for +10 moral