Fire burns next to ice, ice loses. Ice smothers fire, fire loses. You can smother fire with a flamable blanket. The question asked here is very poorly asked.
Ice would win because the fire melts the ice, ice turns to water, water puts out the fire and there is still remains of the ice so yea of course fire loses.
The fire would melt the ice, however if the total volume of ice was small then the resulting water would not be enough to put out the fire, so fire wins.