As long as that doorway isn’t made of wood,

or have any cracks for air to enter the door or doorjam,

that 90% relative humidity should be no problem!

Indoor air during wintertime tends to be low humidity in many places, with most residences running humidifiers to reach a comfortable (~35% RH) level. Clothes-drying will both benefit from the first and assist in the latter.

(California is a notable exception.)

In places which are humid during winter-time, cracking a few windows open will allow for equalisation with the outside, again keeping indoor humidity reasonable.