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The Martian poles are made of both CO2 and water ice.  The water ice is pemanent,  stacked in layers; and reaches a thickness of ~9000' in the North and ~10,000' in the South.  Yes, it does appear that it snows CO2 at the poles.

I would strongly recommend that you read A Travelers' Guide to Mars by William Hartmann. .  It is well written for the layman and should answer nearly all the questions that you ask.

http://www.amazon.com/gp/product/076112 … oding=UTF8