It is a good idea to remove the inside screens from your windows over the winter months. This allows more air to circulate around the inside of the window trim and sill area, thus reducing the incidence of molds and mildews. Molds tend to grow in high moisture areas. In the winter months extra moisture may condense on the colder surfaces of the glass. Adequate ventilation helps expel that moisture.
Although some home owners block off heating vents to certain rooms over the winter months to decrease heating costs, it is never a good idea to completely block off your vents for the same reason - ventilation helps to expel moisture that may contribute to mold and mildew in a home.
When you remove the screens do a quick check of each window and clean the sill and trim if you notice anything that may be mold or mildew. Dry the area quickly after cleaning.
Check for tears and repair any damaged screens. Clean the screens before storing them in a dry area so they will be ready for installation - in case we have an early spring!