I don't know about the limited conflict. I doubt either side was interested in war at the time (though some folks on both sides were itching to 'have it out'), but if the conflict had come, the USSR had little chance of winning a long-drawn exchange with its still crippled economy and badly overstretched forces. If I were in charge of the Politburo, I'd go for the jugular and pray I can parlay the winnings into a new postwar borderline. Of course, the US strategy at the time was aimed precisely at preventing that by basically saying ANY aggression would be answered by nuclear weapons (though admittedly there was some give in that, I doubt it would apply to 30 tank divisions crossing the Elbe)
Given the parlous state of the USSR's economy and infrastructure, the continuing internal unrest in the East bloc, and the inequality of the two militaries, I would assume a brief period of Soviet advances into Germany, Austria and Yugoslavia, followed by a number of humiliating defeats in the air and at sea and the first nuclear strikes against advancing armor. A few days later, the Western forces begin systematically bombing the USSR's strategic infrastructure. Of course, the Soviet air force will retaliate, but until the mid-50s any aerial attack on the US would almost have to be by dint of surprise. Britain, OTOH, is going to get it bad, as is Germany, France, and Italy.
After the first weeks, the counterattack will be marshalled (it might take longer if the USSR can deploy its submarine force to the best effect AND manages to nuke its wish list of Western targets AND they neutralise Germany and France, but that's unlikely. The Red Army at the time would have made a formidable defense force, but I doubt it had the makings of an invader in the face of a decisive defense). I don't think the Soviets had the breath to slog it out, even without continual nuclear attacks against all large concentrations of troops or supplies. Especially early in the 50s, when the Americans could leverage ethnic and political opposition (in case of war, the Ukrainian nationalist groups alone were scheduled to get support from two dedicated bomber squadrons).
The end will look NASTY. Not exactly nuclear winter, but still - think DRC