I'm big on positive reinforcement in training, be that treats or otherwise. As horses learn from association, and think/remember more in pictures & feelings, I believe it's important, invaluable even, to associate what we want of the horse - work, 'right' behaviours - with Good Stuff.
I usually have some treats on me, and in initial training/teaching new stuff to a horse, I do use them quite frequently, but from then on, it's sporadic, more often only given for Extra Special responses... or occasionally just because
I commonly wear a bumbag with treats(& phone, pocket knife, money, etc) & don't give any to anyone for the whole visit/ride.
Having a background in behavioural psych, I well understand how easy it is however, to get timing wrong, to inadvertently reinforce Wrong behaviours due to not being conscious/careful of what it is we're rewarding. Or negatively reinforcing for that matter. Or punishing for that matter.
It's not the specific consequence(be that Good Stuff/treats or Bad Stuff/pressure/punishment) that causes Wrong behaviour,(eg treats DO NOT cause 'nippiness') but we need to be conscious of exactly what it is that's going on at the time of the feedback, to know what we're reinforcing.
I do not want to EVER (as in, regardless what Good behaviour it comes with) reinforce Rude behaviour. I do not want to reinforce my horse expecting or searching for treats, or learning they don't have to do as I ask unless treats are forthcoming.
I very rarely see any value in bribing/luring a horse - that is, offering the treat in order to motivate a behaviour. It can sometimes be helpful in instigating a new behaviour initially. But when used repeatedly, especially if not very judiciously, that IMO tends to lead to inadvertent Wrong lessons, such as grab & run.