You cannot argue with a Wiki link, or an atlas that was quoted for the Wiki page, however I can. After only a short search I am unable to find any reference to the municipality of "Kalt" that dates before 1973 when the district of Mayen-Koblenz in Western Germany was formed. (Via DTS's Wiki Link and then some.) I believe the city was there prior, however nothing online and nothing from my memory or books at hand mention any significance of this city during World War II. I've sent an e-mail to a former Professor hoping to find out more, and while we wait...
You are right that Aachen was the first German city to be captured by the allies on October 21, 1944 and Kalt was not. The map Kalt could be based off the British failed attempt of capturing Tossignano, Italy (December 12-13th 1944 as the date marked on your in-game map is Dec. 13th 1944,) however I believe it is, (and it matches far to perfectly,) loosely based off of the first attack of the German's Ardennes Offensive, (also known as the Battle of the Bulge,) which began December 16th, 1944. It is far more likely a mix up on the creators end and is actually the beginnings of the Ardennes Offensive because Tossignano was a hill top town, (much like Avalanche,) thus narrowing the choices far too greatly.
On a side note Avalanche is actually taking place during Operation Dragoon which landed the U.S. Army's 45th Infantry Division in the south of France at Sainte Maxime on August 15th, 1944. That too is the date on your in-game map however they state "Italy" on the map and I don't believe that just because they throw in a few Italian signs. They also have a vending machine for "Dr>Breens Private Reserve." (Wiki it, there is a church in the middle of the town of St. Maxime.) Now if it is actually based else where, and I pray the developers did NOT do this, then they have fudged the dates so horribly that all is lost and you don't need to bother trying to argue the point any further. The only major action that happened in Italy was the taking of Florence on the 12th of August and from the time I spent there I cannot see Avalanche taking place there or in the hills on the outskirts even. Granted, there isn't really much in the hills.
Now the only reason I'm taking it this far is the reason I even play games like this is my deep tie to history and focus of study on the two World Wars as well as ancient warfare, so for them to butcher it would be heresy in my eyes. The accuracy they have displayed other wise is decent when taking everything into account but I don't know... There is something I must get to the bottom of. And with that I would like to thank you for this post, I've decided to announce that I will take my free time and devote it to giving Edge a definitive historical account for DoD:S. And yes I do have the credentials to do this but don't really want to flaunt that fact.
On another side note, if anyone reading this would like to discuss or ask questions regarding other related topics, (games included,) please feel free to PM me or add me via Steam and I'd be more then happy to answer, expand on or time-line something for you.