I too am having the same problem, using Logitech G400. I can navigate every menu with no issues but when I login and start multiplayer into my group's server I cannot move my character with my mouse. I can shoot, aim down the sights and zoom in but no matter how much I move my mouse. My character will not turn.
Tried it with defaulting controls, revalidating arma 3 and turning off the logitech software.
All with no avail.