[The Might]

Potatoes are in my opinion and good and at least plausible explanation and it would make sense there were taters in Beleriand.

Talking about climate I took a look at this wonderful book that is The Atlas of M-e by Mrs Fonstad and it appears that in her opinion the region where the outlaws lived, as anyways pretty much all of southern and central Beleriand was a region where west winds blew, much like todays Europe and thinks that a type of Gulf current-like oceanic current brought warmth to Beleriand. This results in mild summers and mild winters and in England, North Central Europe and West Oregon (examples given by Mrs Fonstad).

Now, given these circumstances I don't see any problem why the roots could not have been potatoes.