Bicycle tires are party to the same types of deterioration as automotive tires. As soon as the tire has been take off the mold, the rubber compound will begin gassing out volatiles and essentially "drying". As the rubber dries, it'll begin to harden, which will have a negative effect on traction and rolling resistance. The flip side is that "aged" tires also don't wear nearly as fast new tires, if that's something someone would consider a benefit.

For us who live in challenging climates it's suggested that car tires should be replaced every six or so years. After six years even the best winter tires will get hard enough to be essentially useless in low friction conditions even if there's plenty of tread left.

I try to maintain the same cycle of replacement with bicycle tires. If I don't wear through them first that is. The tires I use these days are thin enough that I can usually wear through them way before they harden too much.