I am a boarder not a BO, but am the owner of 2 horses... One is a hard keeper and on is an easy one. The hard keeper is senior, needs lots of grain, and makes a very dirty stall. Easy keeper gets one handful of grain and immaculate stall.
I have no problem paying for extra feed for my senior, but as far as being charged more for extra shavings, no. The stalls are cleaned once a day, no more. If my senior makes a mess, then he stands in it until cleaning time. (Like yours, during the cold weather they are in at night and out during the day unless weather is severe.) the perk for my BO is that my easy keeper only needs his stall cleaned out every 2nd or third day, just picked out inc wet spot the rest of the time.
So as far as bedding goes, as a boarder I feel that an extra wheelbarrow of shavings a few times a week falls under the realm of reasonable care expectations.