"Oak and Ash and Thorn" comes to mind, as do all the "Holly and Ivy" (Christmas) songs. Are you familiar with those? Jean Ritchie wrote a lovely song called "The Holly-Tree Carol", that compares the holly with the beech and oak. There are many versions of "The trees they do grow high", or "Young, but a-daily growing", but trees are only mentioned in the first line. There's also the old ballad from the Makem family about a young girl with child, thrown out of her parents' house, that has the verses:
The taller that a young tree grows, the bitterer (sweeter grows) the bark
And the fonder that a young man speaks, oh the falser is his heart
For he'll kiss you and embrace you
'Til he thinks he has you won
Then he'll go away and leave you
All for some other one
So come all you fair and tender maids
This warning take by me
And never try to build your nest
Up in too high a tree
For the leaves they will all wither
And the branches, they will decay
And the beauty of your own first love
Will oftimes fade away
I like these verses because they shed light on a problematic (to me, anyway) commonplace floating verse that you find in everything from "Fair and Tender Ladies" to "On Top of Old Smokey", about not placing your love on a tree, lest it wither and die.
Another floating verse, most often associated with "The Water is Wide", talks about "she leaned her back up against an oak", etc, that I always took as an allegory for a love that proved false (which it is), but, you find it also in most versions of "The Cruel Mother", which points to the very ancient tradition of seeking a guardian tree under which to give birth. Which is why so many births are associated with the "greenwood side" in folksong.
I've always been interested in folksongs that mention trees and look forward to what others may add.
The song quoted above is in DT as "Month Of January." -JoeClone 19-Jan-2001.