Why laundry dry up also in cold/frost? When you have frost, water in the clothes should freeze, but if clothes are dry, then it should be possible that steam in the clothes does not have time to freeze.
Probably because, initially, the clothes and the liquid water trapped in the clothes fibres, are both at a temperature well above 0 C.
And it does, when the temperature of the garment and water trapped within it have eventually reduced to below 0 C
If clothes are already dry, the situation is not relevant to your question of how (wet) clothes become dry (or dryer) when air temperatures are below 0 C.
If you move warm wet clothes into a cold environment for a sufficiently short time, the water will indeed not have time to freeze. The temperature of the majority of water will not be sufficiently reduced.
Left longer in air at a temperature below 0 C the liquid water in the clothes will freeze and any water vapour in the clothes will form frost.
It is called sublimation. It is how ice cubes disappear in the freezer.