You're not the only one in that boat.
I'm in Iowa and its been cold and bad weather every day for a while.
Here they like to toss sand/salt on the roads and do little plowing at all, so you can imagine the mess it creates.
I gave my daily driver the full detail just before the snow fell last year, and take it to the local Auto Wash every week to keep it clean.
The Auto Wash I go to does great at washing, fairly well at keeping swirls and blemishes to a bare minumum, and it also has a thorough hot air drying system- which is the big plus for me with the cold!
Here's the real kicker- it does all of the above and....
It's not exactly touchless! :eek
The owners of the wash do however, maintain the wash system quite well, which is probably why it works so well.
Even so, for 2-3 months out of the year, I can live with some very minor swirls in exchange for a clean car.
It's a love-hate relationship.
It's back to another full detail and hand washing once spring and better weather are here though.