this isn't entirely without foundation. cold air holds less moisture than warm air. in this country cold air tends to be very dry air therefore less likely to produce any snow.
Very little fresh snow falls at the poles, compared to peoples perception. Most snow in the air is wind blown old snow. As stated before there is very little moisture in the atmosphere so not much new snow falls in polar regions.
Sorry, I wandered from the original question. Yes it can snow below freeseing but is less likely to the colder things get in fairly dry air conditions such as those over the Uk most of the time.