What a great view from your patio (and right on the water)!
Note that we went to Paros in December and the entire island was quite dead. We were probably 2 out of maybe 5 tourists on the entire island at that time. The great majority of restaurants and attractions will be closed even though the weather will still be okay (60+ F). If you like the feeling of being in a very beautiful, remote place, then go in their winter season!