Well, most years the snow starts about July 15 . . . after the previous winter's snow has ended around July 4.
Okay, now seriously, it varies. You could get the first substantial snow any time from late November to early January. I would suggest planning your trip for some time from about mid January to late February if you really want to be sure of seeing a good blanket of snow covering the ground. Depending on the winter, you could get that thick snow cover a lot earlier than that, but there will be winters when the serious snow begins kind of late. You need to get a bit into January to be just about guaranteed of seeing a good covering of white on the ground. Similarly, at the end of winter there is a lot of variation as to when the snow disappears. Some years, you could be here in the middle of March and still see a decent snow cover, but other years the meltdown happens earlier, so again, just to be sure of seeing some good snow cover you probably want to be here before the end of February.