What if soviets attacked Western Europe right after WWII:
1) Soviet forces successfully advance to Europe, using the experience of four years war against Nazis.
The Red Army in the battle hardened, lead by experienced commanders and using blitzkrieg tactics (remember at the defeat of the Kwantung Army).
Experience is important but remember that the US and British beat the "battle hardened" Germans as well. The US battle doctrine was designed to smash up a Blitzkrieg assault by flexing like and elastic band then delivering it's reserve forces to the decisive point. Not only that, but the United States employed it's substantial artillery assets in a more efficient way than the Soviets, who suffered from poor communications until the end of the war.
2)Heavy fighting for airsupremacy. Western Air Forces superior the Soviet Union in the number, but dogfight at low altitudes not their specialty.
That is not relevant since German planes - all designed for low-mid range altitude got absolutely wrecked from above by USAAF planes. The key problem with making a low altitude fighter is that high altitude fighters can dive on them and climb again. - By the end of the war the Allies had developed a robust mobile RADAR system that allowed their high altitude fighters to climb long before enemy planes were anywhere near the front.Add to this the fact they have all of France to climb mean most of the time the soviets would be scrambling to catch up. It's one of the main reasons why the Soviets made a lot of their Jets high altitude interceptors with a fast climb rate.
Not that any of that mattered, when we look at statistics in the Korean war it becomes clear that the battle hardened sovi.. I mean "North Korean" pilots were not of the same calibre as USAF pilots and were shot down 2 to 1 conservatively or 10 to one based on pilot reports.
Start bombing of Soviet cities, the Soviet air defense in general weaker then German. As long as it does not affect the course of the war.
What was left to bomb? In 1945 most of Russia was rubble, the only things the west could of bombed were the industrial sites in the Ural Mountaians
3)American and British bombs kill many Soviet citizens (remember the Dresden).
Soviet propaganda uses it to incite hatred in the Red Army. The main slogans is: "They are not better than the Nazis!," "Prevent a recurrence in 1941!"
The Germans used that sort of propaganda to try to keep going. It worked about as well as pinning medals to 12 year old "Storm Troopers" in Berlin '45.
4)Without air superiority Western forces are forced to retreat (remember Ardennes).
Prisoners nazi return their weapons (including tanks, planes and etc) and sent to the most dangerous areas Red breakthrough. This slows down Soviet Army advance, but can not stop.
The Allies didn't have Air superiority in 1945 they had Air Supremacy. They held this Air supremecy until the 60's when Soviet Air defence got modernised into one of the best in the world. In 1945 the Red Air Force didn't have the fangs it would later develop. Suffice it to say that they wouldn't of had any problems dealing with the Soviet Airforce and would of gained Air Superiority, but not supremacy.
5) Americans throw nuclear bombs on the largest mass of Soviet troops. It destroy big pice of Europe - Germany, Austria, Belgium, France, Norway. Remains unaffected Spain and Italy. But it's up to radioactive rain fall.
One of the bombs dropped on Moscow, but Stalin, of course there is not.
Based on USAAF target priorities and Operation Unthinkable we know which cities the US would of bombed if Stalin got uppity. We know that in June 45 they could only hit 9 of these targets due to limited ready stocks. The plan was to devastate Moscow, Nizhny Novgorod, Kuybyshev, Sverdlovsk, Kazan, Novosibirsk, Omsk, Leningrad and either Saratov or Stalingrad depending on the reconstruction of the latter.
6) Start a new Hundred Years' War. Both sides hate each other and seek to destroy at any cost. The Americans and British people see in Communists the new treacherous Byzantines.
The soviet people see in West the inhuman capitalists willing to do anything for the enslavement of the world.
Europe is divided. Some hate English and Yankees for the bombings, other blamed Communists. The Soviet Union and Allies using this to their advantage
The United States had no intention to bomb France, the low countries or Germany as they were perceived as allies. The US unlike the Soviet Union maintained it's alliances through trust unlike the Soviets who ruled through invasion. See France withdrawing from NATO vs Hungarian Revolution.
From a strategic standpoint it was impossible for the Soviets to push further than the Rhine with their 1945 Army, they lacked the logistics, the communications support and in the case of the USAF bombing their major transport junctions with atomic weapons, the strategic mobility to move as rapidly as required.
The US was by 1945 freshly resupplied and was very lightly resisted in Western Germany compared to the Soviets. Add to this fresh technology finally coming to Europe from the US the US was at a technological advantage, remember it took both sides until the 1950's to really reverse engineer all their captured German tech.
However the war would cost billions of dollars and like Frencho said, Anglo people don't like fighting long wars. Not because of the casualties per-say, but about the money we loose. WW2 cost Britain and the US so much they've still got some of that debt today, continuing to fight was unappealing because of the cost of fighting. The US industrially could produce quadruple the amount of tanks the soviets could if it didn't need to make new aircraft carriers. Problem is that's another year that people at home can't get a new car. By '45 most Americans were driving 1939/40 models. If they had the ration tickets to drive them at all! So truth is it was unthinkable for two reasons;
1) most of the US allies were exhausted and besides Britain didn't really view Communism/Socialism as a threat.
2) It'd be too damn expensive for said Anglo sphere people to endure.