Can I just walk around Greenland with a UV light and find rare Earth minerals on the ground?
I think the answer to your question have to be no.

Lots of minerals are fluorescent in UV light,You can take a look here https://geology.com/articles/fluorescent-minerals/ 

So as you can see in the linked summary of fluorescent minerals it can be hard to tell what you have found unless you know what to look for.

A better way to find Rare Earth Elements might be to use a Geigercounter,Many of the Rare Earth Elements can be found toghether with radioactive minerals.

Here is an example from Norway https://reeminerals.no/fens-field this is an area not far from where i live.

As you can see in the linked article this area can be seen using detectors from an airplane,Maybe not to tell the composition but it can give a hint about where to look.