What are some good tires to install for riding the roads in snow, ice, other winter conditions? Besides letting some pressure out for better traction, what tires should I use?
Snow and ice are two entirely different conditions.
For snow more or less standard "mountain bike" tires are generally fine. Lowering tire pressure is NOT usually a good idea.
For any amount of ice you need studded tires.
Different tires for different conditions.
For bare/wet roads I've been real happy with my Continental Grand Prix 4-Season with Vectran tires.
With snow, it depends on the clearance through your brakes... On a typical road bike with standard brakes, you may not have enough room to add tires with traction. If you have a cyclocross bike or bike with V styled or even disc brakes, you can put on something with a bit of traction for snow and packed snow conditions. I like the Challenge Grifo 700x32c Black/Brown Clincher. On my mountain bike, I love to ride in the snow and use Kenda Nevegal tires.
I tend to not ride in icy conditions, but you can create your own 'studded' tires with zip ties. About every 2 inches cinch up a zip tie around your tire and rim.