If it's a long ride for recreation, I wouldn't wear eye makeup. If it's a transportation ride, and therefore probably a shorter distance, I'd wear whatever makeup was appropriate for the destination.

Since I live in NYC and my transportation alternative is the subway, which can be very hot in summer, I'm used to dealing with sweat and makeup. Cycle or Xootr (my likelier choice) are probably less sweat-inducing than a long wait in a steamy subway station.