It depends on the situation & the horse
Carolyn Resnick (my horse training heroine!) trains her stallions with carrot rewards, but there are very clear rules. She teaches that if you feed a horse a treat the wrong way, he thinks that he took it from you, and you lose rank (from his point of view).
At the barn where I board my horse, there is a very wise "no hand feeding the school horses" Rule to keep the kids safe.
I give my 11yr gelding treats for many good behaviors, and taught him the word "Da!"(Russian for Yes) like a clicker sound, so now he knows that when I say Da he did something I wanted ... But after he has learned the behavior, I gradually phase out the food. I now say Da often for good tries and actions, but only follow it with food (handful of feed, piece of apple) when he has done something exceptional in that moment, or if he was really trying and was close to a positive mental break-through with a behavior I was training for. He also gets a treat when he stands motionless while mounting (I recently had reconstructive knee surgery so I need him to be steady! :P) I will eventually give random rewards for this when he's further along in his training.
I have him for 5 months now, and since learning about the Waterhole Rituals (created by Ms. Resnick), he companion-walks at Liberty in a 100' long arena, walk/trots/turns/halts/ up/jumps in synch with me on my right side.
Using food judiciously has gotten him this far.. not as a bribe, but as a consequence of following my lead/listening/honoring my requests. I'm in Heaven with my Arabian, Prince Sahran!