The flat-spotting you describe is a well-known problem with bias ply tires. It's much worse in winter because it takes them longer to smooth out. Some guys I know use bias ply tires in the warm months and radial tires in the winter.

1977 CJ-7, fiberglass body, AMC 360 w/ headers, DUI ignition, Edelbrock intake and Holley 4150 carb, TF999, Dana 300, 4.56 gears lockers, York air comp, 4" susp lift, 2" body lift, BFG 35" M-T tires, Megashifter, AGR pump & box, REP8000 winch.