You need to let people know what zone your in before they can advise you, also what material is your strawberry pot made of?

Yes they need to be kept moist, maybe about once a month water, depends on soil, light, etc. You cover them for a consistent temperature. My in ground strawberries I cover once they freeze. it's the thawing and freezing that kills them, so the cover helps maintain a more consistent temperature. I don't cover the ones I overwinter in pots in the garage, but it would not hurt to cover them. I may cover them this year as a cold winter is expected.