All i can tell you is that my sister used to ride on the common near Stroud. There are even horses turned out there. The only thing you have to watch is that they are generally full of rabbit holes!
There are very few areas of land that are truly common land, most land belongs to somebody and to ride there without permission or a bridleway present may be trespass unless you can prove access permitted freely over a good number of years.
To be sure of the situation speak to the access and countryside offices at your local county council, or your local BHS access representative.