Neither side would ever consider invading the other.
Russia is simply too massive to invade AND occupy.
And Russia cannot, economically, afford to field its forces in large enough numbers to hold onto Europe.
There was a report by a commission that stated Russia could roll over the European NATO members within weeks.
- What do you think of China as a country?
- If North Korea has a thermonuclear bomb, why is the delivery so important?
- How do countries with long land and water borders in hard to reach areas like the Arctic in Canada and Russia, Tibet in China, Amazon in Brazil, Sahara guard and control their borders from enemies and immigrants?
- Would the US invade Mexico if Mexico doesn't pay for the wall?
- Are Scotland and Ireland friends?
What the report fails to address is what happens when the US moves to a total war footing and comes over in force. The report posits that if it comes down to risking an all out war with Russia and losing Europe, America won’t have an easy choice and may balk. But if the Russians invade and the US kicks into high gear, nothing short of nuclear weapons will be able to stop them. The United States military is simply too powerful for Russia to fight outside of Russia itself.
NATO forces would certainly get bloodied up in the counter attack, but Russian military doctrine against the US is prodigious use of A2/AD strategies. These are overlapping passive and active measures by which you make it so costly for an enemy to advance through an area or territory that they choose to simply avoid it. But these measures only work when they are built up and ready. Russia can’t pickup all of their defenses and move them West.
Outside of Russia, Russian forces will be decisively defeated by NATO forces once the US arrives in force.
The US and the UK and NATO would not seek to conquer Russia (a fools errand) but rather they would structure their operations around trying to remove the teeth from the military so it could not conduct offensive operations for the foreseeable future.
This is all conventional warfare wise. If it goes nuclear there is no secret to the strategy. Fire at will and see who survives.