Maybe it was a slang term that soldiers used because of the means by which Trotsky was killed. That event happened less than a year before Germany and the Soviet Union went to war.
His Grandson and I were flipping through a book I had gotten on WW II armaments. He came in behind us, didn't say anything when I flipped past the German guns, but when I hit the section on Soviet submachine guns, said "Russian Ice Pick. Saw many of those," or something to that effect, and a few other comments on how much he hated the Russians.
Up to that point I didn't even know the man had been in the war.
Later, his daughter told me that that was the first time he had ever alluded to anyone of having been in the German Army. He fought in Russia, was captured by the Soviets at some point, and didn't make it back to Germany until the 1950s, being one of the lucky few who actually survived Soviet captivity.
He apparently reveled in the dissolution of the Soviet Union combined with the reunification of Germany, and died about a year later.
The cartridge did originate with the 7.63x25 Mauser, but it wasn't in use by Germany (at least much) during World War II, so it's very doubtful that he would have had any reason to call it the German Ice Pick.
"The gift which I am sending you is called a dog, and is in fact the most precious and valuable possession of mankind" -Theodorus Gaza
Baby Jesus cries when the fat redneck doesn't have military-grade firepower.