The US already has direct colonial control over NATO. NATO is fully committed to not let Russia invade Greenland or setup oil rigs off the coast, and it is absurd to suggest that Russia or China are patrolling Greenland or have any desire to attempt to take their resources without cooperation. But the US would get NATO's help for defense of Greenland, and NATO would permit greater US contribution to NATO command bases there, or obey orders to contribute more themselves.

Trump, in addition to repeating the false China/Russia threat, has admitted zero interest in Greenland's resources. They are too far away and extremely expensive to develop. This leaves only a single possible motive for needing US control over Greenland: The absolute certainty that EU will disobey US orders for greater submission and the need to directly threaten them from closer distance. There is no offensive missile threat to Russia provided by Greenland relative to other NATO territory.