It'll be narrower and harder, so more likely to cut through the snow. You will reduce the contact patch by increasing pressure (think about what happens to overinflated worn tyres), and that can make it enough to cut through.
That said, and Doc's own experience backs this up, you can happily try to drop the pressures massively too: That's the easier thing to do, however you then run the risk of the tyre spitting off the rim when you drop it low enough to make a difference. Most people would drop the pressures, simply because it's easier to remove air by the side of the road when in a drift than add it!
Winter tyres are always preferred in the smaller sizes because of this. The compound is softer to warm up quicker, that's all. Same reason I run the softest 888s I can on the MR2.