I think it's however you want to count it as long as you're consistent. So if you decide to count the warm up and cool down, then always do that. Warm up and cool down is always a part of exercise, IMHO.
When I enter my exercise into Fitday, I only count the actual running, but that's because exercise is divided up into categories like running at a certain speed, etc. I think if I were just counting exercise just as "exercise," then it would be any time I was moving.
Women who behave rarely make history.