I don't like hunting with people I don't know well and this question is one of the reasons why. There is absolutely NO reason to have the safety off unless in the motion of shooting at game, target.
Years ago I made plans to grouse hunt with a buddy. We meet at the appointed place and time, he's got 2 other guys with him, which wasn't part of the deal. One of them has a brand new gun case and gun, vest and hat. He's wearing cycle riding gloves and keeps smacking his fist into his palm saying "I can't wait to blast something today!". His muzzle constantly swinging around with no regard for where he was pointing it. I should have just left, but we went out hunting. While hunting in a line four abreast first he was straight behind me a lot, then he's walking out in front of me when I'd slow down to watch my dog work some cover. I told him about walking in line, etc., and in reply he said he didn't want to bust brush and there was a trail there. I called the dog, we did a right turn and I left them. Waiting back at the truck the other two come out to the road and walk over. I ask where them where their buddy was and they replied he'd been behind them a few minutes earlier. Just then a grouse flushes from the woods and a couple seconds behind the guy walks out. They ask him why he didn't shoot and his reply was that he saw the road, figured he wouldn't see anything and so turned on his safety. He'd been walking behind me and the other guys, careless with his gun and the safety off the entire time. Could have shot someone in the back. I told them I was done and left. Later I chewed out my buddy. Life's too short to go hunting with some careless greenhorn and get shot.
I primarily shoot an O/U these days. It's easy to catch the thumb safety while busting brush, etc., so I constantly check it to make sure it's on. This fall I took out my old trusty Rem 270 Wingmaster for old times sake. First bird went up and I don't even remember flicking off the safety. It's ingrained, a subconscious movement after years of repetition. I've had instances in the past where my fingers were so cold I couldn't feel them, but the safety came off as needed. Reflexive movement.
I advise you make having the safety on at all times an ingrained habit.