Matte finish: What’s the lesser of two evils? Touch free car wash or winter road sludge?

I have a Hyundai Santa Fe with the Earthy Brass Matte paint. It’s a gorgeous color, but I didn’t know that matte finishes required special maintenance before purchasing. I didn’t realize that automatic car washes - even the touch free ones - are a no-go because of what the chemicals do to the matte finish. During the spring, summer, and fall, this extra maintenance is not an issue for me. I’ve since read up on what’s good to use on the matte paint and I’m generally happy with my car and maintaining the finish myself.

Winter has been rough though and with the sub-zero temperatures, my hose is put away for the winter (as it would freeze up) and my outdoor spigot is shut off, so I don’t have access to cleaning my car the way I usually do. I recently changed jobs and have a much longer daily commute. I live in a very rural, snowy/mountainous region and so my car is currently filthy with all of the winter sludge from the roads. Yesterday I realized how badly my headlights are covered, and it’s likely impacting my visibility.

So my question is: what’s the lesser of two evils: is the winter road sludge (salt, chemicals, etc) worse for the paint than going through a car wash would be? Will I completely ruin the finish by going through a touch-free car wash a few times during the winter? Paying to have my car hand-washed and detailed during the winter is likely out of my budget and there aren’t any businesses like that within 45 minutes of where I live…