The main problem is that Trump is an uneducated man. He is neither worldly nor sophisticated and is definitely not versed in science. He is good at making money with other people's money in deals he bullies them into. That's it.
So, when he hears the words "rare earth", he thinks "gold rush" because the "rare" attribute must mean there isn't much of it and thus it's worth a fortune. Except, that's not the case. Rare earth are not repeat not rare. They are all over the planet in reasonable quantities, including in the US. They derive their names from the fact that, contrary to most other minerals, they are almost never in high concentrations anywhere, so you have to dig huge amounts and carry out a long and complex refining process to get any useful amounts out of the ground.
So Greenland (like just about everybody else) has known sources of rare earth? Well, Woopdy-doo! it's under hundreds, if not thousands of feet of ice, and then you still have to dig huge open air pits of it to bring huge amounts of basically rocks to a refining place that can convert it into a small usable amount of rare earth.
Nobody is doing that right now in Greenland because it makes no economic sense when you can do the same in a hundred if not thousands of other locations that are not under an ice cap.
They have a good setup in Northern NY. I’ve flown with the 10 CAB folks and they have a good grip on whiteout ops as well as the usual brownout that more southern U.S. divisions experience.