Look at the DOT number printed on the sidewall. The last 4 digits represent the date that the tires were manufactured. This is a good thing to keep track of because rubber WILL eventually dry rot and crack, its just a question of when.
(See pic below: Example, "4104" means that it was manufactured in the 41st week of 2004)
The only reason I say this is that the tires could be even older than you think. A lot of tires sit in a warehouse for MANY years (I've seen up to 7 years) before ever being sold to a customer as "new." Trust me, it happens more than you may think. That means yours could be as old as 20 years and, frankly, I wouldn't be caught driving on 20-year-old tires.
If you really want to be sure, you should have them dismounted and look at the inner lining. If it is not cracked and the shoulders are not cracked, then you are good to go for a while.
My $0.02 this snowy morning in Denver (supposed to get 10-18 inches!)