Def change rugs, it also gives you the perfect opportunity to check your horse over for cuts and scrapes, and i wouldn't like sleeping in my wet clothes.
We use the FAL dual purpose rugs so they stay in the same ones. Always make sure we take them off and put them back on again morning and night though to check them over thoroughly and ensure the rug is fitting correctly.
I use fal and Rambo so also keep them on at night most of the time. If the horses are in for a while then I would use stable rugs. Old rambos can be used as stable rugs if they lose their waterproofing which can happen in time. I have yet to have a Fal lose its waterproofing but would guess it would be the same.
If it is very wet I always check the horses are dry underneath their rugs and would change them if they were wet.