A sweet, heavy, dark beer. It should be similar to a porter, but with less nuttiness. They should have a higher alcohol content, not so much for the alcohol itself but as a result of a higher sugar content before fermentation. Sweet malt flavor is usually first and foremost. I don't know if you get Pyramid beer in the Midwest, but their Snow Cap is a perfect example of this style. Some winter beers are closer to ales in color and taste, with more of an emphasis on malt than a normal ale but still hopped like a normal ale. These would include Sierra Nevada's Celebration Ale, and IIRC it is sold nationwide. Mostly it comes down to beers that are too heavy to enjoy during the summer, but are great for sipping next to the fire. Imperial Stouts and Barley Wines are not classified as winter beers, but they are also great for sipping. They are very heavy, and usually have 8% alcohol or above (12.5% in the case of some barley wines). They are meant to be drank at 50 degrees F, so make sure and let them set out for about 15 minutes before drinking.
Christmas ales are a subset of heavy winter ales, and they are similar but include extra flavoring such as pumpkin, anise, orange rind, etc. Think of them as hot apple cider but with beer instead of cider. Anchor's Christmas Ale is one of the most famous here in the west, not sure if it gets a nationwide release.
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