I think that military tires are fine as long as stated above, they aren't cracked, bulged,or show any other signs of odd wear. I wouldn't take a chance on something I planned on driving at 70 on the freeway for hours on end however, but at lower speeds and less use than say a passenger car, I wouldn't have a problem. I have seen older tires separate and come apart under hard use if they were very old, even when they appeared OK.
The main reason for not using old tires in my experience is that the rubber tends to harden over time and become less tractive. This is especially so in motorcycle tires and we won't sell or install anything over 2 years old period. They lose their ability to "stick" to the road. Of course, this is more critical on two rather than four wheels, but just the same it is an issue.
"Free advice is worth what you pay for it."™