The reason you should always wash your car often when driving on salted roads is because the salt gets splashed up onto your vehicle.
That salt then lingers on your vehicles metal body and frame and then eventually the cars body and frame will rust away because of the corrosive salt.
So if you drive often over roads that have been salted in the winter and especially if the roads were slushy with salt then wash the car at a car wash or at home.
I would recommend going through a drive through car wash to get the underneath of the car washed as well so that the salt will be washed away.
It's cheaper to wash the car more often than it is to replace the car.
I would wash the car at least once per week to remove the salt which should be enough.
I've had cars that rusted out when I lived in an area where the winter weather was brutal and they salted the roads often.
The salt corroded out a truck frame of mine before and caused it to rust away where I had to scrap the truck after around 8 years of driving.