I Practice both ways. Walking the quiver is on and arrow on the string (You just never know..........shot a doe and a couple of grouse walking around). In the stand quiver is off, hanging on a hook.
no quiver. they can act like a sail if its windy and cut off your vision through the side of the bow you have it on.
Less wind drift while aiming and shooting! I remove the quiver as soon as the bow is pulled up into the tree.
I tried shooting with my quiver OFF today and my shots were all over the target. I don't know if its a weight distribution thing or what but I definitely shoot better with my quiver on. That is confirmed.
I shoot better with it on but still take it off so I can rest the bow on my lap or shooting rail on it's right side.
I take mine off and hang it on a hook easier to move around when needed but I do practice both ways because we also do spot and stalk hunting but if I am in a tree or a blind it comes off.
I don't use a bow mounted quiver. Less Bulk on my bow and less weight. I carry a small hip quiver in my back pack to hold my arrows.
I've always hunted with the quiver on but this year I am not. I've practiced both ways in the past and never noticed a difference. This year I have only practice with it off. I will be mounting it on my pack.
I take it off once I'm in the stand. I hate clanking an arrow off the rest rest, or piece of gear. I just hang it on a hook of the stand, below my feet. So far, ive never needed a second arrow...
I've did both, however, the past 3 years I've taken it off and had no regrets about it. Just as long as you can still get to a back-up arrow if necessary then no worries.