We're from a very ***cold*** part of Canada, and we went to WDW for the end of January last year. There were a couple of days when we were comfy in t-shirts, but on other days, we were extremely cold. Most evenings and some days, we wore our Canadian winter jackets with fleeces underneath and mitts and scarves. My husband wore three shirts underneath his Northface jacket, and still we needed to go inside to warm up at times. When the wind came up, we were still cold. (We won't even talk about the rainy days.) Seriously, there was even one day that was colder than the same day on the Canadian prairies.
We'd seen the Florida weather forecasts before we left home, and we were unphased, saying, "Well, we know know what _really_ cold weather is like." Seriously, we underestimated how cold it would be.
There were still fun parts, like having the ferry back from Magic Kingdom completely to ourselves.
We still had a great holiday, but I wouldn't be quick to dismiss just how cold it can feel in January.