I just did a quick trip to Italian alps. RyanAir flies to Bergamo (although it says Milan on the website!) And it's pretty close to hills. I just headed up the Brembana valley by bus. Well recommended if you have a few days and want a really cheap trip...
Easyjet flies to Milan Linate and Milan Malpensa - genuine Milan airports. Both airports connect well to the Milan train/bus/coach network. From there to the foot of Monte Cervino (the Italian side of the Matterhorn) and the Monte Rosa Massif is about 4 hours cheap travel.
Easyjet and Ryanair both sometimes fly to Turin, which is a bit nearer the mountains than Milan.
Also to note, although getting buses from the airports to the alpine village is pretty easy, I found it impossible to find fuel in these towns. With a hire car it would be easy enough to get to a fuel station and buy gas/petrol, but when waiting for bus it wasn't easy.
In the end I didn't bother, and just bought salami and bread for my 3 day trip! Next time I probably wouldn't bother taking a stove for a quick summer trip.
Winter would be a different story!
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