It may not be a bad idea to just rinse the bottom of your rig after a drive like that. Maybe pressure wash it or a simple sprinkler/s setup that you can drive over so they're positioned under your car (one each in front, middle and rear) and then just turn on the sprinklers, go inside and have a cuppa coffee for 10 or 15 minutes and that should rinse the entire bottom of your car!
unfortunately drives like that are daily from about December to May where I live haha. But I do try to keep the undercarriage especially clean and rinse it often. I hate salt!!!