Definitely spicebush.
I never thought deer paid any attention to it but last fall I had a doe and 2 fawns hammering the leaves. I had some great pics over on Habitat Talk post #40 of this thread...http://habitat-talk.com/index.php?threads/deer-avoiding-foot-plots-what-are-they-feeding-on.6331/
Yes, some deer eat it. Every herd is different in what they prefer and what they don't prefer.