I'm in Sheffield...south west of the city and very green, considering how close we are to the amenities.
The peak is about 7 minutes drive from my house; the city about the same on a weekday after rush hour, but traffic's appalling most of the time into the city a/m, out of it p/m.
I see the appeal of the hills and the green, but I get all that in the city, so don't feel the urge to go more rural.
I come originally from Birmingham and I really felt the difference in the cold/rain situation. It snowed really badly one winter soon after I moved and I couldn't believe how cold it got! After 18 years, though, I'm finally acclimatised to the northern weather. Either that, or my 'time of life' hot flushes have kicked in Either way, it's working for me!
I sometimes get tempted by the cheaper properties on the edges of the city, Dronfield, Chesterfield, Whittington, etc, as they look beautiful on a sunny day. I'd miss my urban-ness, though. Great buses, great shops, lots to do.
I envy you though. It'll be a cold day in Hell before we move again and even then I suspect it will only be from one part of the city to another. The thought of flitting to the countryside is romantically appealing, even if the reality really wouldn't suit us!
Good luck with the moving...and I'd suggest that driving would probably be a life-saver of a skill in the Peaks, so get those lessons booked!