One more thing to add--please don't hang back and then race up and past other horses! I used to ride with a group in Arkansas and one time there were two younger girls who thought it was hysterial to hang back, then gallop up and past/through the group. This was just great for our poor horses/mules, and they kept doing it even after several people asked them not to. Needless to say, they were never invited back.
If you need to pass others, let them know clearly you are coming up behind them, that you want to pass, and what side you want to pass on (we usually rode logging roads, so plenty room to go by). I usually say something like, "Behind you, pass please, on your left!" Always pass at a walk or slow controlled speed.