Not really. The moisture problem arises if left flat on cold surface that moisture may collect on. Or if left upright, moisture may "wick" up into the slate if it is not up off of the "floor". Moisture alone is not that big a problem. It is the moisture and freezing you will have a problem with.
I had a guy that stored his slates all wrapped up in blankets layed flat on his baesment floor for about 3 years. It took me 3 hours to pry them apart-very carefully. They were damp and moldy but cleaned up just fine. The problem I had was not letting them dry out for a few days before I covered them

The felt wrinkled fairly fast from sucking up the moisture still in the slate. JLK