Here in Poland we can get pretty nasty snow. This year there was a sudden fall of about 20cm with temperatures later down to -10 and lower.
-How do you take care of your car during winter? Especially how do you deal with road salt?
If it gets this nasty wet I try to wash the car every week mostly under the car and wheelarches, pointing the jet washer nozzle under the car to suspension points, etc. Jetwash is very popular here and ever bigger village has one, so it's not an issue and costs only about 1 USD for a few minutes worth of spray
-but would you go on a journey on a road like this with your car
If i had to... the Skoda has the winter tires now (and they do make a hell of a difference, though nothing beats ABS and ESP when it gets compressed-slippery-snow-ice, but my other cars do not. Sadly I had another car with me when the snow had hit... Drive slowly, keep enourmous following distance and aim for well tord places where you have a bigger chance that more cars had churned up the sludge. Also bigger roads get plowed sooner.
One more thing about abs/ esp: I used to live at the end a twisty uphill street. When it snowed in, we saw the first plow maybe after a week. My neighbor managed to get up the hill in his ESP'd Opel family van. (not 4x4) I often stayed on the bottom and walked home as even reversing did not work due to it being so twisty and uphill. Car really hated reversing up.
-What were the drivers doing in harsh winter conditions with their classic cars even without ABS?
Well, they all drove slower. today it's difficult, as the big man behind you in a 4x4 ABS, ESP, SRS and whatnot 200hp Audi will not understand why you want to do 34.5km/h I was taken over in the middle of a snowdrift by a man like that a few weeks ago.
Distance distance, and let them front wheels rolling when you want to steer. that's what i do. Ah, good tires do mean a difference.
-How do you know when to install tire chains before it's too late.
I think when the snow is not yet compacted you can have some chance, but they will not help much if you want to go up on icy road. I tried once and they did the square root of jack, so... I guess it calms your nerves, having them in the trunk, but putting them on in -10 is a turnoff hassle anyway.
I could be entirely wrong here and missing vital education about using them, but i had very little luck generally with chains.