agree with all, likely to be ok w/o a AWD/4WD.
Advantage is that Copper is right by I70, so no local roads to really drive any significant distance.
Disadvantage it that of course it can get a bit dicey on I70 too, but agree w/the prior posting -- look at the 10 day forecast on weather.com before reserving a car -- most times it is reasonably accurate -- and gives you the option at that point.
No real statistics, but believe that more often Vail pass is closed vice the tunnel back at Loveland Pass -- another thought is to get a front wheel drive rental -- tends to be most of the rentals anyway. We have made it up to most resorts in Summit with a van with FWD only -- not sure our AWD would have been much of an improvement.
As per the second note -- if it is really bad enough several trucks will have jack-knifed and others gone too fast and smashed up to get to any resort in Summit county -- guess that isn't what you want to hear anyway. Good luck.