I don't think that the Mongols are proof of the opposite, as evidenced by the fact that they, like "world conquerors" before them like Alexander the Great, failed to colonize the places they conquered, and those places largely returned to their former political systems within a generation or two with very little evidence of Mongol rule. The Mongol state extracted little in the way of wealth and power that didn't come directly from conquest.

Colonization as we know it is more than just conquest and pillaging and setting up a loyalist government (did Napoleon colonize all of Europe? Was Hitler a colonizer?), its a reorganization of the state into an economic tool of the Colonizer country.

There was no colonization or exploitations by the Mongol state that lasted after the figurehead died, while the European colonization not only lasted for centuries, it was reinforced generation after generation with continuing military force and by economic systems designed to basically transform the entire colony and all its people into an economic machine for the host state.

Also, the idea that Europe was constantly at war and other places weren't is very Euro-centric, and I don't blame you because our schools teach ridiculous minutiae of centuries old European politics while not even touching a single iota of say Chinese history or Indian history or African history, so to us, we literally don't know about those regions' and civilizations' millennia's of wars.

Also cold winters, so farming was difficult in northern europe during winter.

People had to store food for winter. Wintertime could be spend on other things than farming, e.g. science.