Shouldn't be a problem
My first suggestion would be to take the cushions off the boat and store them in a dry place. However, I take it from your post that you have no place to store the cushions at home. This shouldn't be a problem. I bought my boat from a guy in Groton, and he kept the cushions on the boat all winter every winter, and sometimes he didn't even cover the boat. Never had a problem wih mold or mildew. My first winter with the boat, I had her shrinkwrapped, put some moisture absorbers aboard, and I left the cushions aboard. I obsessed all winter about the possibility of mold. There was none, but I decided that I would bring them home in the fall from now on. If you do leave them aboard, cover the boat well and put some moisture control in there. Believe it or not, replacement cushions will cost you almost as much as new sails, so treat them well.