How should I run outdoor wiring under my second-story deck?
Provided you follow the same precautions as a NM run parallel to and/or through frame members, such as keeping it a minimum of 2" from the edge of the member, and secure the cable properly to the deck and walls (again, treat it like NM), this is A-OK.  (You'll want to use grommets if you go through metal joists, but again, that's the same as running NM through a steel stud.)

You'll need to put in a surface-mount box for your new fixture, of course, unless it provides its own wiring space (i.e. is volume marked).