I normally hunt with my quiver off the bow. However I practice both ways because you never know when you may need to take an unexpected shot with the quiver still on.
I also practice with it on and off, but I primarily hunt in a blind or in a treestand, and and it's just more to move around to get in position for a shot. The idea for me when I'm getting ready for a shot is less is more...
I have my quiver off when hunting. Mainly because my quiver hits the stand when it is on my bow holder that I use on my summit climber. I try to remain consistent so that is why it comes off all the time.
Until this year, my quiver always came off. One of "these" posts midway through my season made me change my ways. Always on now.