Yeah, I think that describes it pretty well. I don't think I've met anyone else who claims to be able to smell it.
Anyway, as I said, the ozone is produced by the electrical activity in the storm--if you're curious, you can get a smell of ozone off of artificial sources of high-voltage electricity as well. Hanging around a Tesla Coil or Van de Graff Generator ought to do the trick.
And hey, look at it this way, it's not the storm itself you're noticing--you're actually smelling lightning. How cool is that?
I have very poor eyesight, so my hearing and sense of smell are extremely acute.