The skate plays a role as well. The skating boot is equipped with a thin, slightly curved piece of tempered steel attached vertically to the exterior of the sole. This blade ensures that a minimal area comes into contact with the ice, reducing resistance in the form of friction.
The pressure of the blade on the surface of the ice also causes the ice to melt, producing a thin layer of water between the solid ice and the edge of the skater's blade.
"This layer of water gives you very little friction," said Dr. Harry Shipman, professor of physics and astronomy at the University of Delaware. "But if your balance isn't certain and your skates are wobbly, you're going to put more pressure on more layers of water, causing you to slow down. You have to manage the friction as much as you can."
There is a little bit of a perpetuating myth involved here, and this is a good time to deal with this. Many studies have been done in figuring out if the pressure exerted on by someone standing on ice skating blades can actually cause such melting[1,2]. I think this has been clearly debunked. In fact, one can even ask why is the ice still slippery even when one is standing still wearing regular shoes? After all, in such footwear, the contact surface area is considerably larger than skates, and here, it is very difficult to argue for pressure melting.
A very detailed review of why ice is slippery can be found in a nice article in Physics Today by Robert Rosenberg. In it, he showed an interesting phenomenon of liquid-like layer on the surface of ice even at a temperature as low as -35 C. This liquid-like layer is the one primarily responsible for ice being slippery.
Again, common observation/phenomenon can create very interesting physics. That's why I love physics!
 S. C. Colbeck et al., Am. J. Phys. v.65, p.488 (1997).
 S. C. Colbeck, Am. J. Phys. v.63, p.888.
 R. Rosenberg, Phys. Today p.50, December 2005.