I seem to remember reading a few articles about this a couple of years ago (Disclaimer: I'm not claiming to be an expert!)
As I recall, it's not just the weather but also a question of human impact. When Scotland had more trees the climate was a little better than it is today, however the arrival of humans coincided with a worsening in the weather (around 3-4000 years ago I think). Basically in many places it was a double whammy with the forests unable to survive the wetter and cooler (and probably windier) conditions, combined with humans cutting trees for fuel and buildings and then grazing domesticated animals in the clearings.
Without trees to drain the soil and with the onset of a climate change, the soil got waterlogged and acidic and blanket bog spread which meant the surviving trees and their offspring couldn't compete with the grazers (cattle, sheep and deer - whose numbers seem to be out of control in some areas now).
The final blow was the industrial revolution when many of the lowland woods were cut for charcoal, or naval ships.
Still if you go to places like Glen Affric/ Kintail or even Tweedsmuir in the Borders where deer fences have been put up, or extensive deer culls carried out the trees are coming back. I'm not sure how far they will be able to spread given the boggy conditions of much of the highlands today though.
Also don't forget much of the Highlands is maintained in it's state by burning for the grouse, I was surprised years ago to discover exactly how altered and 'man-made' the Highlands is.
Now if we could get some decnt weather I could stop rambling on and go telemarking for a change . . .