This is a foal, right|?? So why on earth would you be thinking of "exercising" a foal?? Sorry to be so blunt but I just think this is silly!! My weaned foals are running around in their paddock. They run and play and, until they are at least yearlings, that is ALL they will do. The two that are in go out to play every day and do just what they like. And, until they are yearlings, that is all they will do. As to "ponying" I have done this with the Arabs- but I always used a smaller pony, (areal Pony!!) and larger mares, I do not think I would attempt it the other way- the little one would be exhausted in a very short while. When he is a yearling- if you need him in show condition, I might use a golf cart- I never had, as I never have had to, but I suppose you could- I would have thought that was for someone who had too many to do singly, and, again, if they are not showing, they just run in the pasture.
Now, Minis with big horses?? Yes absolutely fine, no problems, nice quiet, trustworthy big horses, would not hurt a flea RIGHT UP TO THE POINT WHERE THEY KICK OUT, IN PLAY, AND KILL THE MINI STONE DEAD!! If yo do not mind that happening- and it happened to a friend of mine, and I know someone else on this Forum had it happen, then go on turning them out together- it is OK right up to the point that it goes wrong, there is no room for error- a playful kick among friends would normally result in, at the most, a minor lameness. When a Mini is involved it results in death.