How did the US prepare for the potential of fighting in a Russian winter during the Cold War?

Throughout this period, there were Army troop units (including airborne troops) stationed in Alaska (at Fort Wainwright,near Fairbanks and at Fort Richardson, near Anchorage). This troop concentration usually included either one or two Infantry Brigades with supporting troops (e.g. armor, artillery, and aviation) These troops trained in arctic conditions and in mountainous terrain frequently, as did "lower 48" units which rotated through Alaska for training. There was frequent joint training in conjunction with the Canadian Forces. In addition, there was the Mountain Warfare Training Center at Fort Greely, Alaska (near Delta Junction), through which troops rotated for training. Plus, there was a Cold Regions equipment test center near Fort Greely, Alaska, at which new Army equipment was tested in temperatures extending to below -70 F. The Army of this period was well aware of the special constraints and problems of operating in an Arctic environment. NATO also frequently held multinational exercises in arctic terrain (usually in Norway or Canada) throughout the cold war, in which US forces normally participated. The Air Force also had two bases in Alaska (Eilson AFB, near Fairbanks, and Elmendorf AFB near Anchorage), with assigned aircraft units of multiple types which were well-acquainted with arctic operations). The AF also ran an Arctic Survival School for both Army and Air Force air crews near Eilson AFB. I cannot speak to the Navy elements, though there was a Naval base on Adak Island in the Aleutians. You should also remember that much of the US has a sub-arctic climate, and troop units in the northern states (including national guard units) also gained lots of cold-weather experience. More detail as to units, aircraft types, etc. can be obtained, but the details changed frequently, and I am not prepared to delineate these details, as it would be a very long list, extending as it did over 40 years or so.