It all depends on what you are riding
I have to confess-- I was only trying this out at an event our ski patrol was hosting. One of the vendors brought up to the mountain for folks to demo. The 100 mm tires handled the snow and ice very well. It is a Surly Pugsly. However, I don't think I'd want to tour on it.
Actually, my wife and I planned a route starting in Nordkapp, Norway and heading south to Lisbon. We allowed 4 months, and planned on starting as early in summer as possible in Nordkapp. We did not anticipate any snow. We ran into some visa complications, and ended up starting in Lisbon and never did get as far north as Norway. I'm not sure why you would want to time it so you ran into sub-freezing weather. If you even started in early June, I think you could finish that route by October.
I think Machka's question needs to be the basis for your planning.