The white wispy growths in the photo are normal for this species (polka-dot plant, Hypoestes). They are essentially plant hairs, and some species of plants have more prominent hairy stems (and/or leaves) than others. Sometimes plants kept in high humidity with little airflow develop aerial roots along their stems, which can also look hairlike, but what is pictured looks too fine to be aerial roots, especially since they also seem to be on the leaves (where roots would not form). It is not fungal growth, particularly since that much moldy growth on a plant would result in prominent leaf death and collapse by that point. (The minor amount of leaf tip dieback seen in the leaf at the top of the photo is typical and not related to the stem hair growth. That particular leaf can be clipped off.)

Nothing needs to be done about the stem hairs, but make sure the plant is protected from any air vent or radiator drafts, as houseplants usually are stressed by drafts of warm or chilly air. Warm indoor air in winter is also usually very low in humidity, and indoor plants do best with moderate levels of ambient humidity.

Miri