As a BM myself I will turn my horses out daily unless there is a bad lightening threat then they stay in. Some of the show horses that board with us do not want that and I understand. I leave it up to the individual owner as to whether their horse gets daily turn out when there is a rain threat. Doesn't snow much here so that is not an issue.
No matter what we pick twice daily and strip every week unless more than that is required then we strip it. Daily turn outs seem to reduce the need for more than once a week. We have a shavings barn but when we know it's going to rain we bring in a trailer full of shaving to each barn. If a boarder wants to pick and muck their stall before we get to it, great! The shavings are there for the horses and are going to get used either by us or the boarder so we never fuss over that sort of thing.
I think some BM's get too hung up on the small stuff. IF that is the case I would carry a bag of shavings over there when you know you might be needing it. I have a boarder that uses paper shavings (not sure how I feel about that yet) and the bags are a $1.50 more than wood but you get twice as much. Maybe something to look into as an alternative. Good luck!