Defiantly Driving! While you don't have the feel of the horse underneath you, you sure have the connection with your driving horse.
There are tons of people driving their horses that don't even ride. I don't ride my horse anymore, he was a nutcase under saddle, but he is a great driving horse.
Meadowbrook carts are relatively east to get into, some people use a mounting block to enter their carriages.
What area are you in? I can see if their is a driving club near you that you can go check out. Driving clubs always love to have volunteers around, and they are always ready to help out a beginner.
The best time to plant a tree was 20 years ago, the second best time is today.