We always go in January and it has been a couple of years, but in the past the parks are still very busy until about January 5, but completely doable (we have always been able to do everything we want to do), then start to clear out on/after the 5th.
Weather is a toss up. It is usually in the high 70's or low 80's during the day, but much cooler in the morning and evening. There are also years that it has been freezing! Keep up with weather reports up until the day or so before you go! I usually pack at least one pair of jeans, sweater, and sweatshirt and one coat (just in case), but mostly summer clothing.
Christmas decorations have always been up for the first few days into January. They start coming down around the 4th/5th.
We will be down the first week of January (2-9th) this year too!