*goes to dig out her copy of The Maps of Tolkien's Middle-earth*

Allrightythen. Mirkwood appears to be at the same latitude-type-thing as Eriador and Arnor. I know the south of Eriador doesn't get much snow usually, but the north gets plenty, and by that token I'm assuming Arnor would as well, seeing as it's north of Eriador.

Mirkwood is inland, so it hasn't got the moderating effects of the sea that would generally reduce the amount of snow. Northern Mirkwood, which appears to be the area you're intrested in, has got the Misty Mountains up by its west border and the Grey Mountains on the north border. I think they might also contribute to the amount of snow.

So basically, I think that yes, it would snow in Mirkwood, and definitely around Thranduil's halls. The density of the trees would have to be taken into account- it's not likely that much snow would get through to the ground for the most part, though I seem to remember hearing that the trees thinned out a little around Elven lands, so there might be more snow there.

Hope this helped.