I was in DV last week, and while we did not drive Hunter Mountain road, we hit snow and mud on other passes around 6-7000'. Trying to exit the park to the north on Cucomongo Canyon rd, we hit snow and chained up, but eventually the mud between the snow got quite bad and we turned around so as not to do too much damage to the road surface. We were the first car up there since the snow.
Things melt fast, but be prepared (with an alternative route and the petrol to take it) for snow and mud on the passes. Remember the roads aren't graded often, so if you find yourself leaving ruts, it may be best to turn around.