We have arrived on Jan 1st or 2nd the past three years running. Yes, the weather never fails to turn freezing for that week. This past January was alittle better, actually had days we could comfortably wear short sleeves. Arriving on the 3rd and staying till the 8th will be perfect. We have found that the crowds really clear out beginning on Saturday and Sunday right after New Years Day. By Monday, you will have the place to yourself! The hours shorten up after the weekend and some attractions go into rehab after the busy holiday season, but it's still a great time to go. There will be people swimming no matter what the temp, it amazes me how people, even kids can swim outdoors in 40 degree weather! I guess we Southerners have thin blood or something!
Have a great trip.