It all depends. A knobbly tyre will have a poorer grip on a smooth surface than a smooth tyre, while a smooth tyre will have poorer grip on a loose surface than a knobbly tyre.
But overall a smooth-tyred road bike, on a smooth and clean road, can brake and corner harder w/o skidding than a bike with knobbly tires can.
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On true ice, MTB tyres are only a little better than road tyres. And that improvement comes from softer rubber. But what you really want on ice are studded tyres, something to really bite into the ice and create traction.