What specific war and battle left American soldiers to freeze to death?

I believe American soldiers invaded Moscow, and instead of Russian troops fighting, they waited for all of the soldiers to freeze. And it ended up working for the battle.

First that comes to mind is Bastogne (during and around Christmas time in 1944), when the 101st airborne division was surrounded by Nazi Germany troops during the Battle of the Bulge.

No, Americans never tried to invade Russia. Napoleon and Hitler did, but never the Americans.

For Americans fighting in such conditions you'll most likely come across the Battle of the Bulge.

the Americans were over extended in the Battle of the Bulge and that is where the freezing took place. They never invaded Moscow, That was Germany. From wikipedia

n the West, supply problems were beginning to significantly impede Allied operations, even though the opening of Antwerp in November 1944 did slightly improve the situation. The Allied armies were overextendedâ€"their positions ran from southern France to the Netherlands. German planning revolved around the premise that a successful strike against thinly-manned stretches of the line would halt Allied advances on the entire Western Front.

You can see this portrayed in the Band of Brothers,,,they didnt have winter boots or socks,

I don't know what kinda of alternate history your talking about, but the US has never invaded Russia, ever!!! The coldest climate we ever sent troops to during a war would be in World War 2 in either the battle of the bugle or when the US fought the japanese in the aleutian islands in Alaska (one campaign not many know, but we did fight japs on american soil, go look it up, its very interesting). Some US soldier did freeze to death during those battles, other than that i don't know of any other war were soldier died mainly because of freezing.

You happen to believe incorrectly. The Russians did use that tactic, Russian winter being extremely cold and Russians being extremely unbothered by it, but not against the U.S.. Only Napoleon and Hitler were ever stupid enough to try to invade Russia. Not that American troops never experienced extreme cold. The difficult task of supplying the Allied forced in Western Europe left many Allied soldiers without sufficient supplies in the harsh winter that year