Houseplants slow down in winter, and most problems come from treating them as if it were still summer.
Water less often. Wait until the soil is dry a finger deep, then water well and let the pot drain.
Move plants closer to the window to make up for shorter days, but keep them away from cold glass at night and from radiators, which dry the air and the leaves.
Hold off on feeding until spring. A plant that looks a little quiet in January is usually just resting, and it will pick up again when the days get longer.