If you mean with abridle, just not using the reins, then there really isn't a term for that. If you mean with out a bridle, the term you are looking for is bridleless.
Reins used in western riding
I rode my horse on the left reins around the riding ring!
if you are riding the horse pull its reins to the side to twist there head that way and use the reins to give them a pop to turn around.
The bit on the bridle of a horse, is attached to the reins. The rider holds the reins and thus can control the horse. For example if you pull on the reins, the horse slows down or stops, because of the pressure that is placed on the horse's mouth. Likewise if you pull to the left or right with the rein (this is in English riding) the horse will turn in the direction you are pulling.
the reins (ra.in.s)
When mounted on a horse the rider controls the horse by natural aids such as gentle pressure of the legs and feet. The reins are an artificial aid and are connected to the bit within the horse's mouth. This allows further communication with the horse in order to maintain control.
well with my experience it stops your hands getting sore if your horse pulls hard and wearing proper gloves designed for riding helps yu get a better grip of the reins.
to gather the reins, you take the reins in one hand and grab lower with the other hand, do this with both hands until you have collected your reins to a good length. do not just wiggle the reins through your fingers to shorten them, this is incorrect.
a gag should do the trick also if he snatches the reins out of your hands try grass reins or a martingale!
because when you want the horse to stop it hurts a little when you pull on the reins its a sign that you want your horse to listen to you and to slow down.
That depends. usually, you would simply use your reins to direct the horse where you want it to go or to slow it down. i think this goes for both english and western riding. or you can pull back on the reins to slow it down
I think you mean gloves? And yes, they do. Riding gloves are specifically made to help you keep your grip on the reins. Not to mention if the horse decides to pull them out of your hands it saves you from rope/rein burn. :)