I think that you will be fine. Yes, they can and will tear up the grass and churn it to mud. Since you have a stall, I would look at putting rubber mats in the stall in then shavings, that way you can keep it very clean and DRY!
I would consider stalling your mini. This way you can control his pasture time, keeping him from overgrazing the pasture. You will only have to worry about him tearing up the pasture too much, if you let him overgraze and kill the grass. By keeping him stalled, especially during the wet months, you can watch his feet closely for thrush and whatnot. Also, by stalling him, you can watch his weight very closely, by controlling both his hay and grain, where as you cannot control how much he grazes if pastured solely. If you let him overgraze and destroy the pasture, it will take MUCH longer to repair and rehabilitate your pasture, than to just control his grazing.
Be careful when the pasture is wet. When you let a horse out to excersize they are usually excited and will run and play. Horses can and have slipped in the mud and on wet grass, pulling muscles, tendons, etc.
The only downsize to stalling your mini, is boredom for him and extra cleaning for you. The stalls will need to be mucked at LEAST once a day(preferably twice) and the mini will need to be brought out regularly for grooming and excercize as well as socialization. I think you'll be fine not having a second animal for him, but it means that YOU are his interaction/socialization and you should take it seriously. Try to bring him out (preferably)daily, walk him, brush him, play with him, and whatnot. Also, for boredom, you want to get creative in providing him/her with mental stimulation. Hanging toys that taste good and rattle, provide some play. There are also rubber balls designed for horses that you can place in there for it to play with. If it's possible, give the mini a window he can look out, I've always kept my windows wired so the horses can see out but can't stick their heads out. Look into getting a radio to play softly near the stall to give some background noise. A bored horse can lead to a frustrated and stressed horse. It is why stalled horses so easily pick up bad habits.
Although as long as you provide your mini with attention and toys/stimulation he should be fine and healthier stalled than standing in mud.
-Kim