Are you sure it's not blue smoke as opposed to white? In the given scenario I'd expect it to be black.
Exhaust does burn eyes, and smells, if you're running rich. It burns even worse if it's running lean. Better to avoid it at first place.
First thing I'd do is to pull and examine the plugs. Plugs are your key hole to the inside of a working engine, and a keen eye can tell a lot from a plug inspection alone.
Does your primary O2 sensor, and its surrounded area look okay? Do you have any CELs?
You cat con is in the engine bay, not underneath, so that's nothing to worry about.
Are you suggesting his car's on fire?