The better condition your horse is in, the more he can do. We have a 31" gelding that is medium build. He does cart rides for us all the time and loves it. He can't wait to go once his harness is on. We have to actually hold him back to a walk because he wants to go. If doing rides, he will stand quiet with his head on my (or someone's)lap, but as soon as someone gets into the cart, he is head up and ready to go. We do about 3 min rides and he will do 8 or 10 of those back to back and never slow down and most of the time he won't even break a sweat unless it is a really warm day.
As for the question "Can any mini be taught to drive?" I think that most of them can. We have yet to have one that was impossible, but some had to wait an extra year or two. We try to start them with ground driving in harness when they are about 2 1/2 to 3 years old. Some are not ready and then we back off for sometimes up to 2 or 3 years and do other things with them. We now have one that is 11 and we are finally getting back to working with him and he is doing well. He has been doing saddle rides for us for 8 years, but hated the harness and cart.
Your little mare will do well. Just take the time to know what she is capable of and to get her in the best possible condition for what you are asking of her. She may just surprise you. Just be careful on downhills, because she is only capable of stopping so much. Sort of like putting a 30ft trailer full of lumber behind my little dakota pickup. I might be able to pull it, but Lord help me if I have to stop--especially on a downhill.
Good luck and have fun
Angie