When I am asked about what is safe to do and what is not I have to answer that it depends on the individual doing it.  I have had several clients over the years that taught aerobic classes.  Would I recommend that a pregnant woman who has been a couch potato take up full blown aerobics? 
The answer is No. 
I would recommend walking or a video that was designed for pregnant women.  I would tell the woman who was an aerobic teacher to follow her body's signals and quit or gear down when her body tells her it is time.  It is the same with riding a bike or horse.  The main problem is falling off.  Pregnancy is not the time for mountain biking or cliff jumping with your horse but a gentle horse ride or a moderate bike ride for someone who is used to the sport is probably safe.  I can only say probably because you can not predict the unpredictable and you never know when a horse will be spooked and throw you off or you loose your balance on an unseen pot hole on your bike.  All risk is relative and I have had frantic calls from pregnant women who for no apparent reason fell on their faces.   I also know some women who would laugh if I told them to not ride for 9 months.   
Labor is an endurance event.  Going into labor in the best physical shape is ideal.  Pregnancy is not the time to try to make up for a life of physical neglect.  It is the time to think about your future and start down a road to better health.  Walking and swimming are both great ways to get that start.  After 
your body has time to recuperate from nine months of changes you can increase your activity level.