If I JUST bought the horse then for the first few times in the paddock I leave it on, just incase they are escape artists or the new set of eyes sees a flaw in my security system XD
Stalls, halters are always off and normaly in the pasture halters are always off. I would hate for them to get stuck on something, plus searching for halters in the dark is not my favourite game haha, and the way I look at it is if I need a halter to be able to catch my girl I have a serious problem. I try to teach them to come to me when every they see me with the halter in hand so have never had an issue of playing "catch me".
I find the less halter the better, probably feels good to get it off and doesnt leave marks/indents on there faces that way :)