I have just added a double car garage to my home. The garage does not
have dedicated heating. It does however benefit from a roof and back
wall that are part of the house which in turn prevents freezing in
winter. I did not do a good job in the area of floor drainage. In
winter the ice and snow from the autos melt and the water drains to
the sides and back of the garage rather than out the garage door. I
recognize that the answer most likley is that I should place some sort
of proper drainage . This would be somewhat costly and I am wondering
if there is another solution that I could look at. For exampel
creating a membrain of some description that would collect the water
making it easier to drain off the water from the garage floor.

I found this product. Or you could grate your driveway into a runoff.

The Garage Floor Protection Mat by Better Life Technology, LLC (17 ft.
x 7.5 ft) is just what you need to keep your garage floor clean. The
protection mat keeps your garage, shop, or basement floors looking
like new! The tough PVC non-porous surface has been specially
formulated to protect against oil, antifreeze, salt, and common
contaminates found on garage and shop floors. Available in slate
gray($169.95), forest green($189.95), brick red($189.95), midnight
black($189.95), racing blue($189.95), and sandstone($189.95) colors.

http://www.autobarn.net/garfloorprot1.html

The simplest solution is to probably use a wet/dry shop-vac to vacuum
the water when needed.

I though about that to but it is a temporay solution. Personally I
would just grate it and into a run off or a drain. But if Guilford
dosen't want to go to that much trouble I think the mat would work
great.