If you visit in winter, the cobblestones may be icy. Wear good winter shoes so you don't slip.
A visit to Rauma is great any time of year. The Lace Festival is held in the summer, so if that interests you, plan your visit accordingly. The farmers market is held on Saturdays in the center of Old Rauma and is a really great one to check out.
Winter and summer are great times to visit. Vanha Rauma is usually a quiet town with not many visitors, so you'll feel like you are exploring somewhere off the beaten path. Go early in the morning and you'll have the place to yourself.