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Probably. I can't imagine it would hurt. Friction is a function of the force being applied to a surface and the coefficient of friction of the surface. So the more force you have the more friction you'll get. That's why snow tires work better than summer. The extra treads help increase the tire's coefficient of friction.
It's probably negligible, but heat is function of pressure so more force pressing down on snow/ice will cause the temp. to rise which could lead to water on ice.
But again, this is probably minimal considering the short time any point between the tire and snow/ice is actually contacting each other. Plus the heat generated from your car driving over a patch of ice will probably be so minimal that it wouldn't even be enough to melt the ice any appreciable ammount, especially if it's very cold.
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