As Foxtrot says, use fluids meeting MIL-PRF-5606J. These fluids work down to -54°C (-65°F).
Not sure why he said to use non-aviation fluids. The aviation fluids are absolutely top notch, and very reasonably priced. They are commonly used in bottle and other types of jacks that are used in arctic environments. The main plus for your application is that they are readily available in quart and gallon containers, whereas the Kendall Hyken Glacial Blu only comes in 5 gallon pails and 55 gallon drums.
The two standard 5606J fluids are Aeroshell 41 and Phillips X/C 5606J. They are interchangeable. A quart of Aeroshell 41 costs $12.65 at Aircraft Spruce & Specialty Co. A gallon is $49.50. The Phillips X/C 5606J is $11.95/qt.
The previous spec for these fluids was MIL-H-5606A. It is considered obsolete by the military. The difference is that the 5606J is an "ultra-clean" spec. This is important for an airplane, but not necessary for a jack. The fluids meeting this spec are Aeroshell 4 and Phillips X/C 5606A. Both are still available in gallon containers, and are slightly less expensive than their 5606J replacements. At Aircraft Spruce, a gallon of Aeroshell 4 is $42.50 and a gallon of Phillips X/C 5606A is $46.95.
I'm guessing a pallet jack shouldn't need more than 1qt of fluid. In that case the quart of Aeroshell 41 or Phillips X/C 5606J would be plenty, and won't break the bank.