it all depends where the car is parked. If you drive it out in the salt and snow and then come park it in a warm garage... DEFINITELY hose your car down with water, esp the wheel wells. Or else the snow is just sitting there with salt, slowly melting, so thats basically a mix of water+salt for hoursss on your car. Can you imagine what happens? Rust.
Now if you park outside. You dont need to do anything. Why? Simple. The snow and salt mix is just frozen in place. No damage done to the car. The temperature is so low here that the chemical reaction needed to rust wont occur. However as soon as the temperatures is warm enough to make ice and snow melt.... same principal as before... you better hose the car down completely with water.
Make sure when you wash it, to do it everywhere. Try aiming the hose at your suspension parts, brakes,etc if you want your car to last long..
If you havent rust-proofed it, do that also.
Last but not least, if you want to keep it clean... its hard in the winter, esp if we get one like last year. I used to wash my car once a week, so I dont get high deposits of salt accumulated. But thats just me. Some people dont even do it once the entire winter.