Although I agree that washing the car's underside is a good idea, I wouldn't spend sleepless nights worrying about it. Salt deposits on the open surfaces don't typically do any real damage. The damage occurs in crevices, where high concentrations of chlorine can cause damage. If you look at modern cars that are rusting, you'll notice that the rust is usually adjacent to a seam.
The Corolla uses galvanneal coated steel on all of its exposed and underbody sheet metal components. They are fastened in such as way as not to allow moisture to puddle up. The chAssis receives a phosphate wash, an E-coat, a primer coat, then a base coat. So it takes quite a while for the salt to attack these areas.
A quick rinsing of the underside won't get the crevices, so you may not be doing much good down there. And parking in the street isn't any worse for rust than parking in a garage, unless it is constantly getting sprayed with road salt.
A good, thorough cleaning helps remove the salt. It's important to get the salt off after the temps have warmed up since warm wet salt is far more corrosive than anything else. In fact, dried salt does not corrode. It has to be wet to produce corrosion.