Basically, the further North you go the colder the weather generally is so Scotland, and typically the further Northerly parts get the brunt of the colder weather fronts. Believe me, you would chill in a hurry over even in the Northerly parts of England when Winter kicks in if what you describe would chill you to the bone...
I went and did a little research on Scotland's climate. It looks to me as if there is high humidity with a lot of wind so it would feel really cold even if it was above freezing. Approximately 3 months of snow isn't extreme, and the lowest recorded low isn't anwhere near the lows I've seen.
The year I was born, not that I actually remember seeing it, was so cold the trees were exploding because the sap was freezing inside the trees and blowing them apart from how a liquid expands when it freezes. It got down to -60 F that year and stayed there for several weeks. My parents told me it would snow without a cloud in the sky as it was so cold any moisture in the air froze. I can remember seeing -40 to -50 F for a few weeks straight as a kid. That was one cold winter we spent in Drummond, Montana. It doesn't happen often, but it does happen. I've seen it cold enough when I was a kid that my dad actually built a fire under the oil pan on his pickup to warm up the oil enough so he could start the engine without running the main bearings in the engine dry of oil. I don't remember the actual temperature that year, but it was pretty dang cold.
