All of my horses training and tricks have been taught through pressure and release - no treats needed. Though if she puts lots of effort in she gets a treat or two. Though treats should only be used if your horse respects you and is not pushy in any way.
If you are afraid your horse would misuse it's trick for begging for food, make sure to have a cue for the food. I trained my horse a bunch of tricks with a clicker (mostly known for dog training). That way he knew he would only get a treat if I made the click sound 😊 just start with a small harmless trick such as touching a target or smiling. If he would misuse it there is no real harm done.