Our DOT suggests a limit of 10 years. However, in BC you get about as much sunlight as we do in Western Washington, so 10 years is a reasonable estimate for a limit.
I replaced my tires at 10 years although they didn't look hardly used and had most of the tread left. The tires had about 50K miles on them. We spent about 4 months in Yuma each winter and that may have "aged" the tires more than while up north. We never had any tire problems.
Bottom line though, you don't want to have a tire fail. Most of us don't carry a spare, and if you do, you'll have some difficulty trying to change it. Those things are heavy. A blown tire can cause other damage to the coach and may even cause you to go out of control.
Since your coach is a 2002, I suspect your tires may be more than 12 years old. You may be pushing your luck.