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The explanation that is most likely right is that, even well below the freezing point of water (or the melting point of ice, which is the same), there is a thin film of liquid water on the ice surface, which acts as a lubricant for the skate blade. The existence of such a liquid layer was already inferred in the mid-nineteenth century by the great British chemist and physicist Michael Faraday. Both theory and experiment now agree that ice "pre-melts", that is, that such a layer forms at temperatures well below the melting point of ice. The layer thickens as the temperature goes up and as the real melting point is approached. At that point the whole solid mass, not only its surface, becomes liquid. Going in the other direction, getting colder, the liquid surface layer gets thinner, which is consistent with skating being noticeably harder when it is very cold (as my ice-skating friends tell me!).
The reason the question had been debated for so long is that there were two other competing theories. One, now almost entirely discredited, is the theory that proposed the liquid layer at the ice surface not to form spontaneously, as is now believed, but rather by
"pressure melting". It is the case that ice can be made to melt under high pressure, but no reasonable estimate of the pressure on the ice surface exerted by a person on a skate blade is great enough to make ice melt at the very low temperatures, even down to 30 degrees below zero Fahrenheit, at which skating is still possible. The other rival explanation, melting due to heating by friction between the skate blade and the ice surface, probably does contribute some, but does not explain why ice is slippery even when the skater is standing still. So, we are left with "pre-melting".
A nice article on this subject is "Why is Ice Slippery?", by Robert Rosenberg, in the December 2005 issue of Physics Today.
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