This is a really unfortunate side-affect of people training their horses with treats without understanding HOW to clicker train.
One big thing about food is it's a strong motivator. A horse WANTS to do what earns them food, they want to do it more and better all the time. They escalate each skill you teach them. You can use this to your advantage if you're informed and paying attention, molding skills into bigger and better skills. But if you aren't paying attention or molding the skill you're setting yourself up for failure. Feeding him for invading your space is a skill best saved for a well clicker-trained horse who has a great deal of impulse control and understanding of the language and the rules. If you aren't paying attention you can easily be rewarding behavior getting out of hand, many horses escalate touching with their nose to biting unless you're focused and molding correctly, you can use this escalation to teach them to fetch - but you don't want them fetching your nose!
All of my horses are trained with clicker training, the only one who knows any 'tricks' is my pony who kicks a football, the rest are just learning the same things that all horses learn. The clicker is a bridge signal that says "yes", once they know click=treat they need to learn HOW to take a treat. I start every horse I train by standing at their shoulder with my pouch full of food, when the horse stands calmly and faces forward, all 4 feet on the ground - I click+treat. I work on this until the horse no longer even looks in my direction to get the food. I then start walking around them - the horse needs to stand 4 on the ground facing forward no matter where I go - until I tell them otherwise. Typically I teach them to target from there and use the target to shape all their future skills.
If you or anyone else is interesting in learning how to safely and correctly use clicker training/positive reinforcement with horses please check out the thread. Please learn all the facts and science behind CT - it's a fantastically useful tool but it needs to be done correctly (just like every type of training!) Clicker Training: Challenge Accepted
This is my favorite example of clicker training gone RIGHT! This is my mare, a previously spooky uncontrollable horse who could barely be lead on the ground without explosions. This is us now, learning about tarps this time. (I don't always ride tackless, this was just a special occasion - we were in a safe, controlled environment and I had a helmet on)