Driving at night is best case scenario. way less traffic. They do a great job of keeping the roads clear. The only reason why you wouldn't want to go is if it is blizzard conditions. Make sure you check the weather for loveland pass, because the weather may not be bad at denver airport, and still be a blizzard up there. They can also very quickly put a chain law in effect in that case so watch for that as well. How long it takes depends on where you are going. If your just going to the Dillon area. your looking at 1.5-2 hrs from airport. Breck and copper add 15 minutes, vail add 30-40. Big heads up if your travel plans have you leaving on a sunday. The drive down on sundays are the worst, it will take you 2-4 hours to get to airport so plan accordingly.
Roads can be pretty dicey up there. Generally they do a pretty good job keeping it clean but the approach to the tunnel from either direction can be pretty snowpacked or icy even half a day or longer after it has stopped snowing. Good news is that loveland pass is 100% avoidable by going through the Eisenhower tunnel. As far as the weather is concerned, check the forecast for the whole I-70 corridor not just Loveland pass. Once you start driving into the mountains the weather can change at the drop of a hat (completely clear to nuking just a few miles apart). If the weather cooperates, it should be a pretty easy drive although it wont be nearly as scenic as a drive in the day. A drive in moderate to heavy at night is going to suck and take significantly longer. Check out cotrip.org or call 511 when you get there for the most current road conditions, closures, and chain laws. It should give you a pretty good idea of what to expect.