When it's 14 degrees out, and your car is caked in salt and muck... You do what you have to do.
It will be fine...
Before I knew anything about what was used in touchless washes, I had an 9 year old Malibu LTZ with 145K miles that I faithfully put through a laser touchless once a week in the New Hampshire winters.
Last time me and a mechanic were under the car (Oct 2016) we were both shocked that everything underneath looked almost new. The mechanic said he loved working on my vehicle because nothing was rusted, nothing was corroded and everything was easy to work on.
That told me right there, despite the harsh soaps, and pre-treatments... they did their job. For the metal and plastics on top of the car, I always make sure I use Pinnacle Black Label Diamond Coating or CarPro CQuartz UK and CQ Dlux. When that air dryer hits the car, the water just flies off. I now do the same thing for my brand new Mustang EB Prem.
The only time a wash like this is an issue is on an older vehicle where rubber door and window seals may be questionable. Or a classic car that is prone to rust. Waterless or rinsless washes are perhaps better for a classic or antique. However, those should't have winter salt/muck etc..
hope this helps!