People keep saying "It's too cold to snow," yet it seems to snow quite happily at the Poles, where it must be colder than here, so what is the truth, if any, behind this expression?
When it snows, its due to an area of low pressure, bringing moisture with it which falls as snow. In winter lows are always warmer than areas of high pressure, and so if the weather warms slightly when its cloudy the likelihood is that it will snow (or rain). There isn't a set limit (apart from a ground level air temperature of 2 celsius or so, above which it tends to fall as rain.)