Winter is tough on batteries, for two main reasons. The battery cannot produce its normal amount of power because of the cold. The chemical reactions that generate electricity are slower at a lower temperatures. Checking your car battery from time to time will help you stay on top of any maintenance issues, but be aware that most car batteries only last between three and five years. In addition, engines are harder to turn over because the oil inside them is thicker. This demands more amperage from a battery. Multi-viscosity oils, such as 10W30, though, alleviate most of this impact.
Check the battery cables and clamps for fraying or corrosion. If there's a white, powdery substance around the clamps, that's corrosion from battery acid. You can clean it off easily with baking soda, water and a toothbrush. Your battery contains a liquid electrolyte, which can evaporate and spill so make sure it has enough inside. Most batteries have caps on top, and you can check the level by removing the caps. If it's low, fill the holes with distilled water, being careful not to fill past any fill level indicator or the bottom of the cap.