Wait, what? You know the Winter War wasn't planned in order to capture snow, right?
Reality isn't Red Alert. Stalin was a (generally) effective and conservative strategist.
The US wouldn't ally themselves with the Reich. The way they saw the USSR and the Reich was the same as the way that the USSR saw the Reich and the West: Both as potential threats that are better off expending energy fighting each other.
Although the Bering Sea can be very stormy at times, the US Pacific Fleet is still massive, they aren't at war with Japan yet, and they would only need to detach a relatively small squadron in order to interdict the overstretched Soviet supply lines, and can essentially starve out the Soviet soldiers. They won't be able to mount an effective resistance to American offensives once their ammo quickly runs dry. In other words, the Russians are fucked if they land in Alaska. Now, I don't believe America would have any real ability or inclination to mount a counterinvasion of the Soviet Union, especially from the east, but it would still unnecessarily create a massive enemy that can inconvenience them in many other ways. No Lend-Lease, for example.
Even in some universe where the Soviets successfully captured Alaska, the British/Canadians would almost certainly be outright hostile, whilst Alaska had very little of value (at least that would be easily exploitable for the Soviets).