As a native speaker (American), I have no trouble whatsoever with "snow in the tree". Either preposition is possible, with slightly different meanings. I interpret "... in the tree" as meaning there is a lot of it in every nook and cranny of the tree, and "... on the tree" as meaning there might be a light dusting on the upper surfaces. In this example, I actually prefer "in" as it seems there is quite a bit.
I never get snow at all where I am (California), but I still make the distinction I've described. I don't know how widely this distinction is distributed amongst native English-speakers.
Do other native English-speakers actually perceive "snow in the tree" as incorrect in all circumstances?