it doesn't sound right does it? I guess it's because the colder the air the less moisture it can hold and therefore the less snow it can produce. Also if I can remember this correctly cold air in the UK often comes from an easterly direction, ie continental europe/russia so it won't have have spent much tiome over sea to pick up moisture. I'm now at the limit of my weather knowledge but some of our bigger snowfalls happen when cold fronts meet warmer moister air coming from the west, ie from the atlantic.
I await correction from more knowledgeable types, with pleasure