While it may be a given, it's still extremely important to mention the basics in winter car equipment: You will need a snowbrush and an ice scrapper. Remember, a soft-bristled snowbrush is less likely to damage your paint and plastic scrappers won't scratch your windshield and windows as easily as metal ones. Other tools suited for unpredictable winter conditions include a collapsible shovel, a well-stocked emergency kit and a set of jumper cables.
For mountain regions, add a set of tire chains to your trunk as it may be the only way you'll be able to drive. As well, in case your vehicle becomes immobilized in deep snow you can either buy of set of traction pads or use some scrap pieces of carpet to help you escape those arctic traps -- but make sure you read the instructions carefully prior to using the traction pads as they often have spiked bottoms and can be quite dangerous.
When taking a long trip (a common practice during the holiday season) include items such as a blanket, a flashlight, candles and a lighter, flares, and an extra bottle of windshield washer fluid in case of unplanned circumstances or roadside stops.
Understandably, this winter gear might represent a burden for trunk space, but your preparation may be a relief for you later on.