effectively there are moderately common road/condition combinations that you cannot drive in a rental car.
Where is this? I live in northern part of Scandinavia, and we manage just fine with normal winter tires. Snow chains are pretty much only for semi trucks. Most people even use studless winter tires these days.
And of course rental cars have winter tires in the winter season, anything else would be illegal.
The US does not mandate snow tires at a national level, and in many places (even northern states where snow and ice are common) tire chains are illegal because they can damage the roads.
If you're going up steep hills covered in ice, winter tires or even studded tires are not going to work. You need chains. Then again, the best rally drivers are Scandinavian, so maybe you guys are just better drivers than we are :)
Lots of them in the West. Little Cottonwood Canyon (at a minimum) in Utah. Tahoe from the Bay area (Donner Pass) under certain conditions http://www.dot.ca.gov/trafficops/trucks/chains.html. In a number of cases you can get exceptions for approved winter tires but it varies.