Mine also seems to run cooler when towing and pulling hills. While towing I also have tow/haul mode engaged. I've always pondered if tow/haul mode either keeps the shutters open or leaves them open longer to compensate for the additional thermal load.
I wouldn't try disabling them though as the ECM monitors them and will set codes/CEL for problems. The whole cooling system works as a unit.
Right from the factory service manual
"The Active Grill Shutter (AGS) system is controlled by the Powertrain Control Module (PCM) over a dedicated network Local Interconnect Network (LIN) bus. The Active Grill Shutters perform an initialization each time the vehicle is started. The initialization can be used as a quick way to validate the operation of the AGS. To perform the AGS validation, start the engine and observe the grill shutters. The shutters will cycle to the fully open position and then to the fully closed positions to initialize and learn the hard stops on the grill shutter frame for each key cycle.
If the AGS smart module detects the grill shutters are jammed, it will attempt to free them by cycling the shutters from the open to close positions 3 times. If this condition is detected when the ambient air temperature is greater than 4.4°C (40°F) the MIL will illuminate and a Diagnostic Trouble Code (DTC) will set. If the ambient air temperature is below 4.4°C (40°F) and a jammed condition is detected, the smart module will assume the shutters are frozen and will not illuminate the MIL or set a DTC."