Gently removing snow from tree and shrub branches, keeping bird feeders clean, and checking houseplants for pests are some of the gardening activities for this month.
When tree and shrub branches bend under the weight of a new snowfall, use a broom to gently brush off the snow. Don't try to remove ice or you might break the branch. It's possible to save a branch that partially splits from the main trunk if you tie it in place and use long screws (coming from each direction, if necessary) to secure it. If done right away, the tree may callous over the wound and heal itself next season, and not split further.
Birds deserve clean food surfaces as much as we do. Every few weeks bring the feeders inside and wash them with soap and water into which a little bleach has been added (1 part bleach to 9 parts water). Rinse thoroughly. If you have a heated bird bath, keep it scrubbed and cleaned regularly as well. I keep an old brush handy, just for this purpose whenever I refill the bath.
Aphids and spider mites may be multiplying like crazy amidst your houseplants, especially if they are grouped close together. Isolate each plant and inspect it closely, with a magnifying glass if necessary. Treat these pests by holding the plant and pot upside down and submerging the foliage in a sink full of soapy water (wrap aluminum foil over the soil to keep it from falling out). In severe cases, spray the plant with insecticidal soap.
Look on houseplants where the leaves join the stems for the white masses of mealybugs. Rub them off with a cotton swab dipped in alcohol. If you see brown lumps on stems and leaves, these are likely scale insects. They are hard to control, as even rubbing them off they seem to reappear in a few weeks, so check plants often.