Not sure whether drag and drop works but Copy and Paste certainly does but you must have the two Vegas projects open at the ame time (although one or the other can be mininmised as necessary).
If you haven't started the new project yet, here's what I'd do: Open the old project. Delete everything not needed in the new project. File - Save As to the new project. Done.
This method probably has another advantage. Last I checked (it's been a while), when you copy or drag/drop a subclip between projects it reverts back to its original default name. So if for some reason you've renamed the subclips you'll lose all those names.
I don't think this will happen if you do a save-as.
As others have said it sure would be nice to be able to either
1) Export subclips into Media Manager
or
2) Export (or "save as") subclips from the project media bin to disc as individual .avi files
or
3) Export to some metadata file on disc that could then be imported into another project.