I think you should (in a very calm, mature manner) bring up your concerns with your dad.
I have a few points to make:
- when I'm working with a horse that isn't mine, I will often say "that's my good boy/girl" without even thinking about it. I don't mean anything by saying "my," it just comes out.
- I know with my dad, he's not very horsey, but he tries very very hard to make it important to him, because it's important to me. Perhaps your dad is trying to do the same. I would be just over the moon thrilled if my dad went to the barn to spend some quality time with a horse near and dear to me, without me.
- Have you explained to your dad why you don't like to give treats to your horse? Lots of people do give treats without even thinking - it's human nature. If he is told why you don't like giving your horse treats, perhaps he might be more understanding? Or (if this isn't a health issue for your horse) maybe you two could reach a happy-medium by saying "treats only given in his feeder/special treat bucket."
- Don't sweat the small stuff. Grooming equipment gets dirty, it's the nature of the beast. Instead of getting mad that your grooming supplies are dirty, I would be inclined to suggest thanking your dad for grooming your horse.
- I can understand not wanting someone to yahoo around on your horse - completely understandable... how about teaching your dad how to ride English properly, or suggest taking western lessons? Instead of making it a bad thing for him to ride at all, I would suggest turning it into some positive time together.
I suspect that he's trying to get closer to you, and he knows how important your horses are to you. Personally, I would be just elated if my dad wanted to spend any time at all at the barn with me anymore; that part of our relationship fell off the face of the earth when I got my license, car, and moved out, and I'm terribly sad about it. This is just my train of thought stemming from my personal experiences.