Yes, most use them.
For an arab I'd probably do something to keep it from flying all over the place (assuming it's long?) but you don't have to braid.
I'm with the conservative folks here... even if you're doing jumpers, at a rated show you should be in a jacket and show shirt. I was at a show where the judge requested everyone fasten their collars! (apparently he didn't like it that everyone rode with their collars open) A black square pad might be ok but I usually use white with a dark colored trim. I would NOT do pink zebra! For polos I'd keep it dark and conservative too. Black. Maybe darker navy. Possibly white. I use black or leather eskadrons/equifit boots.