I'm (suprisingly) going to agree with Kevin and SMrobs. It is disrespectful for a horse to come into your space and should be sent backwards out of your space fast. My horses know to shift when I tell them, they dont touch a bucket of feed untill I say as untill I say so that bucket of feed is in my personal space.
My horses are taught that whilst it is alright for them to hang over the stable door as soon as I go to enter it they must back off and they will not get anything untill they do. I can invite them into my personal space and we can have a good scratch and a nice happy time but it is on my terms and my terms only not thiers.
I've delt with loads of abuse cases, loads of agressive horses. I've delt with horses that when I got them would activly attack people. I had one that came over a stable door, picked a girl up by her ear and shook her untill her ear ripped off (that was the reason he ended up with me). I've always backed off every horse I've owned, so that they know I'm the dominant one.
We had an accident on my yard with a box resting horse, I was away at uni so my brother was doing horses and he did not back horses off, little slips in discipline like not getting them to take steps back before they got feeds, allowing the pony to pull at the haynet as it was put up etc, led to a horrific situation with the pony deciding to take leadership from my brother and deciding to kick the living daylights out of him. Took 2 months for his manners to deteriorate, took me 2 hours to teach them again, he never ever did it again.
Also as you are dominant, you have the right to touch the horse anywhere at anytime, the horse is lower in the pecking order then you therefore you have the right to invade his personal space with no conciquences, but he does not have the right to enter your space.
A horse that knows his place and knows the rules is a happy, settled and content horse.