I can't advise you about removing the equipment as I don't close my pool down. If you've already removed I'd just store them inside over the winter. Can't hurt, huh?
I would not clean the cell *unless* it appears to need cleaning. It can shorten the lifespan of the plates if done unnecessarily.
My control box sits outside year round, but in the coldest weather when its freezing overnight (since we don't close) Skippy puts moving blankets and a tarp over the pool equipment along with a hanging auto light underneath and we run the pump overnight. No problems at all with the SWG control box (knock on wood!)