Non-melting ice is ice that is below 0 deg. If the atmospheric temperature is above zero, the ice surface will remain at zero deg, and melt. The thin layer of water on the ice surface vastly reduces friction.
Frozen water tends to be more 'sticky' the colder it gets. That's why 'wet' snow occurs when the temperature is warmer than that for 'dry' snow. 'Wet' snow being snow that can be moulded easily (into a snowball for example), at temps above -15. 'Dry' snow can't be moulded, and has more friction.
At least, that's how I figure it
Non melting ice would be great in my bundy, but sadly the bar has to be sub-zero in the first place.