I have a 2011 F-450 4X4 with the 6.7 Diesel, 6 speed tranny, and 4:30 rear end gear ratio. The truck has plenty of snort to tow our 18K pound toyhauler. I too was disappointed at the sag in the rear with a load on. At the time I opted to beef up the leaf springs and overlaods. I went with a sequential leaf system which reduced the sag but stiffened the ride a bit. We have a Cyclone 3800 HD. We experianced very serious "chucking" when we first picked up our unit. I opted to install a 5th Airborne airride kingpin. That reduced the chucking about 65%. I have ordered airbags for the truck and waiting for the system to arrive and have it installed. Your F-350 should have plenty of power to move most any towable depending on gear ratio. I have not towed this rig in the snow. Frankly, I would not want to.
Regards
CabinetmakerII