Try draining a little out of the sump where the differential is. I am not familiar with the 354 and plug locations but if there is sufficient water in the rear end to freeze up it may be causing your problems.
Also, on the 354, is there a second set of reduction gears out at or near the wheel? If so, there may be a sump to lubricate just those gears. Water/ice in that sump would definitely cause the symptoms you describe.
Since you mentioned that heating the brake area seems to release the wheel, it might be possible that the brake pads themselves got wet, maybe just condensation in the housing. If you park the tractor with the brakes set, and there is moisture on the pads, they could then freeze to the drum.
Assuming you do have brake shoe/drum style brakes, it is also possible that a broken return spring is not pulling the shoe away from the drum when the brakes are released. IF that shoe were wet, it would lay against the drum where it could freeze.
Do you have a parts manual that shows how your 354 is made?
Let us know what you find, and good luck with it!