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1.
Cigars on ice is a phrase used to describe a man taking a cold shower to relieve his boner. Cigar=boner; on ice=cold shower
Beyoncé's song "Drunk in Love"

Cigars on ice, cigars on ice.
by Sexiichic December 30, 2013
 
2.
To perform oral sex on a male with ice.
Cigars on ice Cigars on ice.

Eat the cake, on Ice would be the same, but for a female.
by MilkyWayHo January 01, 2014