A few years ago, my club had Guenther Wendt (The "Pad Fuhrer" of NASA fame) as a speaker.
http://en.wikipedia.org/wiki/Guenter_Wendt
Aside from the Nasa stuff he also talked about being in the Luftwaffe as a nightfighter pilot and then how in 1944 when they started running out of aircraft and gasoline he was transferred to a ground unit that fought in the Battle of the Bulge. Without being sure, I am guesing this can be a reason why you see the guy dressed like this. He may have been a pilot or aircrew moved to a ground unit as things started coming apart alte in the war.
I also remember reading in 'A Blood Dimmed Tide' about how suprised American troops were at the ease which they able to ambush some "Falshirmjager" units.... They aslo mentioend these troops had new equipment and uniforms. So I am guessing it was some of these transformed aircrew and aircraft support people. This also jives with what Mr Wendt told us - becasue I remember him saying he said he was one of only 3 from over 200 in his unit that made it to the end of the battle.
Hope this helps.