Regardless of the actual reality, it was (and still is) believed that the .30 carbine was not sufficiently effective in the Korean winter.
Again, I'd like to point out that "not sufficiently effective" is NOT the same thing as "won't go through clothes". In this matter, I'm quite sure "the tale grew in the telling".
And the belief in "not sufficiently effective" was official. In actions, if not in regulations. I had a friend who was in Korea, serving as a telephone lineman (Signal Corps) for a couple years, shortly after the armistice ended most of the shooting.
He carried a carbine, and liked it. But, when it got cold, "they took away my carbine and made me carry that awful heavy M1 Garand." He didn't like that.
He was also happy to point out that he, personally, had never been in a situation where he had to shoot anyone, and if he had been, his opinions of the carbine and the Garand would be different.
The M1 Carbine served through the winter of 44-45 in Europe, and didn't get a reputation for not getting through heavy winter clothes there.
If you look at enough incidents, you can find freak occurrences where EVERYTHING has failed to do its usual job one time, or another. A lot of these have a perfectly rational explanation, IF enough additional facts are known. But, when they aren't, (or are, and just don't make it into the story), these kinds of tale get started, and embellished.
Adm. Kimmel was struck by a Japanese 7.7mm machinegun bullet, that went through his office window while he was watching the attack on Pearl Harbor. The bullet was spent, and bounced off his uniform. He was quoted as saying, "it would have been kinder if it killed me."
The Jap 7.7mm didn't get a reputation for being worthless because of this.
There was an American officer struck by an 88mm Tiger tank round. He survived a grazing blow to his neck. Nobody made up any stories about the 88mm not working.
But, lots of other stories got, and still get made up, and widely spread as "gospel". I cannot tell you the number of stories I heard about the M16 and what it could, or would not do. A couple of them actually did have some relationship to the truth, but not a very close one.