Here's a quick tutorial on how to get out of Nightfall on Extinction, Call Of Duty Ghosts. Simply go to the spot where i do on the map: Climb on the railing Crouch down Strafe jump off over the railing. If for some reason you can do it like this you can make sure you have Feral Instincts boosters equipped and and then press down on the D-Padd to deploy them right before you jump this will make it easier. The Feral Instinct booster must be equipped and you need at least $800 to use them. You can also get back into the map by walking through the barrier you jumped over! Here's the Video : http://youtu.be/tOLzOT3cPYI Credit to whoever found this.
I know man, there's a fair area outside you can run around too. Just remember to shoot the floor when you are running around and if you don't see and dust or snow fly, then its not safe to walk on.
Easiest way I found is to have Feral Instinct equipped and upgrade it to max level, so kill some aliens for a while until you can max it out, that way you jump right out of the map easily.