We have a strong weaved cover on our hoop house and we take it off every winter - it is easy to do and it lets all that moisture into the ground from the snow.
We don't have any heat in there but just having it covered gives us a couple weeks extended growing season and some seasons it is just what is in the hoop house that will thrive. This year was terrible for peppers and tomatoes with the cool and wet but they were fine in the hoop house.