Air at a given temperature can hold only a certain amount of water
vapour: the colder it is, the less it can hold. In cold weather, this
saturation level is so low there is very little water vapour in the air,
even if the relative humidity (the ratio of the amount in the air to
the saturation value) is high.
The rate of evaporation from a moist surface depends on
the difference between the concentration of vapour in the air right at
the surface and the concentration in the bulk of the air. The former
depends on the temperature of the moist surface: in the case of your
skin, it is warm even in cold weather, whereas the vapour concentration
in the bulk is low in cold weather. So evaporation takes place at a
higher rate than in warm weather.
This is true even in a heated building, because heating
the air that has come in from outside does not increase its water vapour
content. Humidifiers can add water, but they consume a lot of energy.
Large buildings sometimes have systems that can transfer water between
incoming and outgoing air, which are more energy-efficient.
Though water evaporates faster from your skin in cold
weather, your laundry dries more slowly. Because it is not heated by
your body as your skin is, the level of water vapour right at the
surface is quite low, so the rate of evaporation is low too. If you want
your laundry to dry quickly, wear it.
Eric Kvaalen, La Courneuve, France