Some do, some don't. My boy races to the gate when he sees me, my mare was totally unconcerned (although would let me catch her easily enough).
As long as you always make the process a pleasant one, your horse will start to associate you coming to the field with something nice and may start to take the initiative and come to you.
I have found, however, that the enthusiasm displayed by horses for being caught diminishes in direct proportion to the amount of grass in the field