Some more tea questions: why is caffeine in black, while green is known as healthier?

I just read a helpful post about the differences between green and white tea, and it made me realize I also have some tea questions! Here they are:

1. If black, green and white teas have the same amount of antioxidants, why is green tea known to be "healthier"? Is there something else that green tea, and perhaps white tea, has that black tea does not?

2. If the only differences between black, green and white teas are the length of time they are brewed (thus fermented, right?), why does black tea often have caffeine and green tea does not? Caffeine occurs naturally in tea leaves, right?

3. Any difference between hot and cold tea? I love to make sun tea, and then ice it down.

4. The antioxidants in tea: are these the same that are in red wine?

Thanks!!