I leave the halter on with a lead rope attached if it has a purpose. For example if I'll be out on the trail for hours and might want to get off the horseback and walk for a while to stretch my legs, or sometimes I cross areas where it's too dangerous to be mounted, boggy areas or scree areas, then I want to get off and lead the horse by a leadrope and not by the reins. If I loose my balance walking in such areas I might jerk the horses mouth if leading by the reins and I don't want to cause the horse pain. It's also handy to be able to tie the horse safely if you let him wear a halter and a lead rope.
I do anytime I'm not in an enclosed space. What if something happened to my bridle? Its much easier in an emergency situation to have some sort of backup. I use an english bridle with no noseband and I usually run the throatlach through the cheekrings on the halter for extra security. On my english saddle, I tie the leadrope with a quick release to the buck strap that I made for my baby cousins.