A typical workflow for me is opening Vim (MacVim to be precise), doing:
:NERDTree
then manually opening various subdirectories
Sure just save the session with ":mksession ~/mysession.vim". ":mks" works too. Then just source the file and there you go.
Unfortunately, there is no way to do this in NERDTree - yet. If you feel like the feature deserves attention, however, you can add it yourself or submit a request for it on GitHub, and it will be available to you soon.
Edit: I took the liberty of submitting the feature request myself; you can track its status here.