How to store over winter

We usually push the Duster outside, put jack posts under the frame and put on a fairly good car cover and use tie down straps to hold in on (in three places) because it is windy here.

Now that the car has been nicely painted..I am rethinking this..I think I can have the cover washed at the dry cleaner folks but I am worried about the tie down straps and the wind.

Would it be better to just let the show pile on it ?