I wouldn't recommend putting a mini in with an average sized horse for many reasons. Everyone that I've met with minis keeps them separate from the bigger horses.
Introduce them carefully but after that they'll be fine. The mini where I board is actually the bully and all but one of the horses and ponies are scared of him. Also the mini picks up all the hay the horses drop that would usually just be wasted so they really aren't expensive companions.
I would watch them very carefully at first. It should be ok as long as you are attentive
My big horse is a bully in the pasture but doesn't kick or anything. He just bites and makes mean faces. So I guess it will depend on how he reacts
It all depends on how your larger horse reacts with others in a social setting. They'll probably be more dominant, but unless they're really aggressive towards other horses it shouldn't be an issue.