Looks more like an electrical problem with the fuel sending unit in the tank. I work for Audi in Colorado and when the cold hits this is not very uncommon. Electrical components can do some funky things when cold weather is involved. Probably not the answer you wanted to hear but its likely. I had my sending unit replaced the first winter I owned my WK for the same problem.
2006 WK, 4.7L V8, Flowmaster 40 Series, RK 3.5 Xfactor, 255/75/17 BFG Mud Terrains, K&N Air Cleaner, Bilstein front struts, Rocky Road rear shocks, 4XGuard Front Skid