We used to go the first week of Feb years ago and loved it. Very low crowds, although now I'm sure it is busier than years past, but still considered some of the lowest crowds of the year. We walked on rides over and over and at times it seemed we had the parks to ourselves.
Weather can be chilly, but nice for park touring. We wore sweatshirts and were fine. I actually prefer the cooler weather for walking around all day as opposed to the exhausting, blistering heat of summer.
As far as refurbs go, I would not let that deter me at all. Things are closed all year round, even in the busy season, not just the winter time anymore. It seems you wont find a time when everything is up and running.
Water parks were not a factor for us as we do not go to the water parks, but for some it might make a difference.