The information others have given is good, but a little abrasive.
I agree that putting minis out with the larger breeds can be dangerous for all the reasons given. But if you are comfortable with it and you are willing to take the chance of something adverse happening, then that is your call. I know several people that allow thier minis out with thier larger counterparts and they get along well. Yes it is possible for the larger horse to injure and possibly kill a mini.
It can be just as dangerous to put a young foal out with other herdmates, that are not its mother. I had a filly that was kicked by another mini and it broke her lower jaw. We were able to wire it and it came out fine, but it taught me that horses will be horses and that injury can happen in all situations. Yes, it is a bigger risk with the full size horses, but again this is your ultimate call. Just make the decision based on your comfort zone and always take into consideration the welfare of you horse.
As far as exercising your weanling. Natural exercise is the best.... remember in the colder months your horses will become more sedate, conserving energy. Yes, there again could be underlying issues, such as illness, worming issues, nutrition issues etc, but all of mine are in excellent health and they just tend to be more quiet during the winter months. If your filly stands with her head down and looks dull and listless, off feed, then there could be illness issues, ulcer, depression. If she is active and moving around her pen with her head up and she is alert when you are out there and eager to eat and greet, then she is probably just fine. She is much better out in a larger pen with a shelter than inside in a stall.
I am sure you are doing the best with her, and if you have any questions, have someone that has experience in minis come look at her. Or if it is a possible health issue have your vet take a look at her and at your feed program.
