I apparently am the first person in the world (!) to report this real bug to Apple regarding their newest version of OS/X (Snow Leopard): cannot drag and drop photo into Address Book.
I noticed it when trying to drag and drop from iPhoto, but it also doesn’t work when doing it from the Desktop. Apple didn’t promise to fix it, but I suspect they will.
Meantime, the work-around is to drag the photo out of iPhoto (if there) onto the Desktop. Then in Address Book, double click on the space for the photo and go through the buttons presented to “choose” the file from the desktop copy.
Update 11 Nov 2009: Apple’s update to OS X Version 10.6.2 fixes this problem.