However, I would not take too much notice of the NPS website when it comes to this road. It can close at short notice any month of the year - even in summer. At that altitude, over 12000', blizzards roll in without much notice.
The best thing to do is check with a visitor centre when you get close to RMNP - and even that is no guarantee. It was in Sept 2009 when at 4pm I was assured it would be open the next day. By 6.25 that evening the Trail Ridge Road was closed by a blizzard.