Watch this science video tutorial from Nurd Rage on how to compare regular ice with liquid nitrogen-cooled ice with Dr. Lithium.
See how to take cubes of regular ice and cool them with liquid nitrogen.
The ice made this way can be used to cool drinks and as long as you don't let the ice directly touch your mouth the drinks are safe. Once they warm back up to 0 degrees they can be treated exactly the same as regular ice.
Alternatively, just use a straw when using ice of this type.
Brought to you by one of WonderHowTo's favorite scientists, NurdRage.