Having clean wash media is always important, but even more so when the sand/salt hits the roads.
FWIW, I hit the DIY wand wash or a touchless drive-thru anytime the vehicles are heavily coated with road crud. That happens year round in my part of the country due to the gravel roads that are often a part of road construction.
After rinsing off the majority of the road grime, I then finish the job at home.
Most often with a rinseless or waterless product.