If I do leave them hang it's in a building were wood smoke is. If that closet is in an out building that pretty much is like being outside then I'd say go for it. If it's in your house I woudn't do it.
I have a closet where I keep my clothes in an out building, it's also where the wood boiler is which is next to the chicken coop and wood shed, in a woods.
Rarely does any of my gear come in the house.