Aye, yon place is quite weel-kent. I like the bit about the Scottish soldiers, 'when the spring came, they started looking for women' - obviously they introduced linkie-hunting - though I can't believe the Italians hadn't already thought of that sport!
Likewise, they may deny eating haggis, but actually that was an invention of the Romans - they more often made it with pig's offal, but sometimes with sheep's, which would have been pretty much the same as the Scottish version.
As for the climate, it's probably a good bit warmer in summer, but they're well up in the mountains, the scenery looks like the Highlands on steroids - so I dare say they get some snell winds and probably plenty of snow in winter.
I think the core of the story is probably true, though it's been hyped a bit for the tourist trade. That there were Scottish mercenaries fighting in the wars in the Alps is well established - it even prompted us to pirate Rossini's tune, relocate it from Switzerland to the Tyrol, and make it into a good pipe march with some moving lyrics: