What does the red color that my characters get painted occasionally mean?
The red color you are seeing on your character indicates that you are being Vision Pulsed by an enemy Recon character. The Recon characters special ability (called Vision Pulse), is essentially a wall hack for the entire other team to use against you. It allows the entire enemy team to see you and your teammates for a limited amount of time through walls.
Note that this is not unique to the hardcore game modes. It can happen in regular game modes as well. To give you an idea, this is what it looks like from the Recon's perspective who used the Vision Pulse:
