I actually run my BFG Mud terrains at 50psi in the city.
But never that much on the trails...
Really, you can run up to the max tire pressure printed on the sidewall and probably be fine. But like you say, your cornering and braking may be negatively affected. If 35 to 37 PSI does not exceed the tire pressure max on the sidewall you'll be fine, and probably get a few more miles/km's to the tank...
