It depends on the combination of how long you've been there and how much you care.
Last US leg, I got up and showered where we were staying at 4am and was in line by 5am. I don't really care about hair and the usual sweatiness (it wasn't even a warm day), but I HATE having a greasy face so before the line was squished together around 5pm, I rinsed my face w/ my extra water bottle and some face wash I had in the car. My friends were smirking and saying I was primping for Bono, but seriously, I'd wash my face before going to work or out for lunch or something.
Other people leave and go to apartments or hotels to shower, or nearby gas stations or restaurants. To me, it would only be an issue if you were in line for 24+ hrs.