Derbyshire winters?

A fairly common meme in fanfic is that the winters at Pemberley are much worse than those at Longbourn (including a great deal more snow), but I've never been able to confirm that. After all, it's not very high: the highest point in the Peaks District is under 2100 ft, and this is apparently only 1100 feet above the average height of the region. The mountains between my house in Palo Alto, CA, and the Pacific Ocean max out at 3800 ft, and the elevation here is about 20, yet no one I know would say the winters in the mountains are 'much harsher' (the juxtaposition of 'harsh' and 'California winter' is absurd when referring to coastal areas). The only weather data I could find is fairly recent, and the amount of snow in the Peaks region is apparently LESS than that in London (although there are more 'snow days'), and it was colder in the 1800's than it is now, so I don't feel I can draw any conclusions from this.

But it makes me wonder if this meme is based on some faulty unconscious mental model - such as the one I have, where I think of "the south of England" vs. "the north" as being like Florida vs. Maine, when it's less than the distance between Santa Barbara and San Diego, where the climatic differences are fairly minor. Of course it's only a couple of hundred miles from New York to Boston, and when I moved between those two cities as a kid, I was very surprised at now much colder the winters were, so maybe the 'meme' is correct...

Can anyone set me straight on this? Thanks.