Pregnant women are told to do and not do all sorts of things, so the knee jerk reaction most people have to this is "No! Of course not!"
Most horsemen will continue to ride and work and even show mares until they are about 6 to 8 months pregnant. Reasonable exercise during pregnancy (obviously, riding a mare to exhaustion might threaten the foal) is actually beneficial and helps the mare be fitter to handle labor.
After that point, the fetus grows rapidly and affects the mare's balance, plus it becomes rather unfair to ask her to haul around the weight of a foal and a rider. Saddle fit can also become an issue. Mares that have had at least one foal tend to "show" more and sooner than first timers. (In fact, the horse world is full of stories of people riding a mare, turning her out, and then arriving the next morning to a foal they had no clue existed).