The Yaquis and Apaches would have been more of a problem. Spaniards never really conquered the Yaquis. And the Apaches once gave the US much to worry about.
The Mongols, seem to only go where there was enough grass for there horses. No grass in the Tundra for there horses. They did sometimes use ships to invade islands but generally it usually went bad for them.
Just look at the map of the mongol invasion. They never conquered way up north.
See this Map:
http://upload.wikimedia.org/wikipedia/commons/2/28/Mongol_Empire_History.jpg
But if they had managed to get to North America they could have conquered part of it. Must remember there were not that many Mongols. They were overstretched in Asia and Europe.