So this is a lot later than I intended, but I do have an answer, at least in response to Russia.

Bandy, a sport similar to hockey, has been played in Russia for centuries. It uses a larger ice surface (closer to the size of a soccer/football field), and has more players, but is a close enough relative.

First a bit of background on the sporting landscape of the USSR: In the early Soviet Union, sports was not seen as a vital part of the socialist lifestyle. It was considered bourgeois, a pursuit of people who had a lot of free time (which late 19th century sports effectively was; class played a major role in the development of sports, as can be evidenced in the amateurs-only rule for the Olympics when it was started, for example).

This had started to change prior to the Second World War, but only really came into its own afterwards. The Soviet Union look at sports as a means to export communism, by showcasing the superiority of the communist/socialist (I use both terms here interchangeably) way of life, in that it could produce far superior athletes. Thus the USSR finally joined the International Olympic Committee in 1951, and of course would utterly dominate both the Summer and Winter Games until the end.

Now, hockey had been known to the Soviet Union since the beginning. Neighbouring countries like Czechoslovakia and Poland had been playing it since it first came to Europe just after the turn of the century, and the sport was very popular in Germany. I don't have the book on me, but Lawrence Martin's The Red Machine explains this.

However it was not until 1945 that the Soviet authorities first properly came into contact with hockey. This came about, oddly enough, from a series of soccer matches in the United Kingdom. FC Dynamo Moscow toured the UK in the fall of 1945, and prior to doing so had bolstered its roster with several of the top Soviet players, the most notable probably being Vsevolod Bobrov, who was with CDKA Moscow (later renamed CSKA). I also believe Anatoli Tarasov was with them, but again I don't have Martin's book on hand (as I'll note, it is the authoritative account of Soviet hockey). While in the UK the Soviet players watched some hockey matches, and were enthralled with it. As NHL President Clarence Campbell would later remark, "This was the time when the Russians got the idea for their hockey team. The Russian soccer players were more interested in watching Canadian players play hockey than in soccer." They purchased their first hockey sticks on this trip, and went back to the USSR with the idea to develop "Canadian hockey," as it was initially known there.

It would be 1946 when the Soviet league was established, with all the matches being played outdoors. Most of the players were either soccer players, bandy players, or both, having been brought in to try out the new sport. Unsurprisingly many of the tactics used in those two sports were incorporated into Soviet hockey, such as an emphasis on passing and skill, and speed over brute strength. Though they wanted to enter the World Championship in 1953, an injury to Bobrov (who would excel at hockey, much like he did in soccer), saw them pull out at the last minute, and instead make their international debut in 1954. They surprised the world by winning gold, and would start a reign of excellence in hockey that effectively lasted until the demise of the Soviet Union.

It was a combination of exploiting the popularity of bandy, the international success, and the establishment of sports as a major component of Soviet society (boarding schools for "athletically gifted" children were established in 1956. By 1970 over 5 million children attended these, which were largely feeder systems for the senior clubs). In a way it did prove the idea that socialism was good for sports, as the Soviets were able to effectively create the world's strongest hockey program from scratch in a matter of years (this of course ignores the issue of them being "amateurs" and not competing against the top Canadian players), so it was one of the major successes for the USSR.

As noted, the key book on this is Lawrence Martin's The Red Machine: The Soviet Quest to Dominate Canada's Game. It was published in 1990, and is the definitive account of Soviet hockey in English. Unfortunately it's been long out of print, and hard to find now, but it is a must-read for anyone who wants to understand the topic. Martin also wrote it in a very authoritative way, in that it's not exactly a pop history, nor a dry academic tome, but sort of in the middle. Either way, a highly recommended book, and a shame there isn't anything else like it out there.