Sgt. Nash was the man leading Alex and his team when they were ambushed. They were both sent back to a hospital in the states due to severe injury.
In an unnamed hospital, Alex and Sgt. Nash keep a good relationship while their wounds heal, Alex remarking "He's a good man."
Sgt. Nash leaves the hospital about a month before Alex does. He expresses disappointment that the army is only letting him spend a few weeks with his wife and daughter before he is back on duty. The last words he says to Alex are "Don't trust anyone."
In the finale of the game, it is revealed that Alex's military past never happened. It can therefore be presumed that Sgt. Nash was a figment of Alex's imagination.
Despite being a character out of Alex's imagination, Sgt. Nash is mentioned considerably more than other real-life characters in Alex's diary.
Alex talks about how Sgt. Nash saved the team from an ambush and how Nash would be proud to see him walking without crutches or a wheelchair. Nash, like Alex's father, is a military man and he may represent the mentor Alex wishes he had.
Sgt. Nash leaving Alex with the warning "Trust No One," may represent many things. It may refer to the citizens of Shepherd's Glen (suggesting his father told him the town's dark secret). It may refer to the doctors and nurses who are keeping him confined. It may even refer to Alex himself.
It is also possible that Sgt. Nash was a real man. Nash may actually have been an employee at the institution. This would explain why Nash feeds Alex's delusion about the war and why Nash was released, whereas Alex was not (their location being a mental hospital.) This can be observed by him helping Alex in a fatherly way and giving Alex someone to trust inside the lonely hospital.