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And what you are exeperiencing is completely in line with the physics of your basement.
But even at a 'normal' 30-35% relative winter humidty, the fact that your basement walls below grade will remain at a relatively constant 55degrees F but the upper portions of your wall can and will drop to nearly the -25C you are experiencing only goes to support the fact that the upper walls are cooling the air below the dew point while the lower walls are not.
For example, at an interior temperature of 70 degrees F and a relative humidty of 35%, the dew point (Condensation point) is only 40 degrees F. Any surface that cools below this level has the potential to create condensation and icing.
Obviously your upper walls are well below 32F or 0C since the condensation is freezing only above ground, and not below.
If you have open web concrete blocks for your basement walls and the webs remain open at the top, this will only add to your existing problem.
The reason is that ground water vapor will enter the block cavities, move up and out of the block cavities at the top of the wall thru convection, increase the relative humidty in these pockets below the subfloor and the top of the block wall, and increase condensation and the dew point.
The only ways you can reduce this problem is to dehumidify the basement, add foam insulation on the outside of the house foundation above the ground, and to fill the webs in the block at the top of the wall to block moisturef rom entering the basement.