I grew up in Maine; everybody in winter drives a white car, regardless of what color it came from the factory. About once a month in winter, my dad would take his car (a Saab) to the "you hose it" place, pump in a couple quarters and wash the underbody with the power washer. Never touched the body, always the underbody and wheel wells. Put close to 300,000 miles on that thing in ten years, finally gave it up when the tranny went. The dealership he sold it to replaced the tranny and sold it faster than the cars they were pulling from Florida, not a speck of rust on the thing.

Just wash it down, you'll be fine.

(Of course, I drove a '74 Volkswagon Beetle that never saw 80k, because it got washed NEVER, and I could put my foot through the floor boards, the rust was so bad. It finally died when I ran it into a snowbank, didn't wash it out, and rusted out the body pan where the control arm attached two years later!)

 

Most of the quarter washes (coin wash, whatever you call em), have mag-chloride remover foam and heated water.

I usually bring a spray bottle of simple green and a "wheel" brush (kind of wide but still flexible).
Hit the underside with the mag chloride remover with the first $1.25, brush like crazy, use simple green to clean extra dirty stuff, and then rinse everything very thoroughly with the heated water (dissolves salt on its own).

Dont forget under the hood, my PO neglected to rinse anything off and as a result even the top of my fuel-rail is extremely rusty