I googled calcium chloride density and hit a Dow Chemical brochure that was very information filled.
http://www.glchloride.com/brochure/Broc ... ndbook.pdf
If you look at the phase diagram, 30% by weight is the perfect concentration to minimize the freezing point and gives 10.79 lbs/gallon liquid density. More than that and the freezing point starts rising very quickly.
For 300 lbs of calcium chloride in each cub tire, you would have to net a density of 23 lbs/gallon, or approximately the density of aluminum - you can't get there from here...