Thoroughly interesting read from all of you thank you for writing in this thread.
I think sometimes we like to play the what-if military thought games and we head out into the realms of the improbable. But we all know the improbable leads to the possible sometimes :/
I don't think there isn't going to be any sort of 'hot' war anywhere any time soon with any first world countries, just not going to happen (although we are happy to keep building weapons systems to fight the last war we never fought). Sadly we'll continue to see "third-world" countries obliterating each other's populations at a low boil for decades to come. Hundreds of thousands of people dead across Africa, Iraq, Syria, and a lovely slow soft war in Eastern Europe that will continue for a long time. As pointed out earlier none of the big boys are getting involved, we're happy to sell to the combatants or fund proxies.
Regarding Europe as a defensive military vs Russia on it's own in a fantasy non nuclear conflict, it's game over in quick order for a short campaign. Europe's forces just don't have the numbers, and more importantly the massively complicated command and control and force projection required for today's sort of fighting. The Russians are quite good at this sort of thing, and it's Borsch in France in a few weeks. Remember the Libyan air campaign recently? The Euro air forces couldn't do much of anything on their own and were about 100% dependent on American command and control, coordination, and pointing out where the Europeans put the bombs. This was not widely reported in the press because this was supposed to be seen as a 'European' leading campaign, but it was basically run by the Americans because the Europeans just don't have the air hardware and coordination to run those sort of sorties. It's not a slight on the Europeans, they are (perhaps wisely), spending that money on healthcare and public infrastructure, and we spend it on fancy AWACS.
And let's be honest even at the -height- of the cold war, there weren't nearly enough NATO ground forces to do much more than be cannon-fodder to slow down Russian armored advances until a full mobilization could occur or before things escalated to nuclear. This is a similar situation in South Korea; there's enough North Korean artillery and missiles pointed at Seoul to basically obliterate the civilian population and the small US/Korean force on the border in a surprise attack. This doesn't mean that NK won't be absolutely crushed if an actual campaign gets going, but the first part of the conflict those border troops are forfeit.
The same thing in Europe, if it started the actual 'long' war would be about beating back Russian forces from their full advances gained early on.
Now that I actually read more or less about that kind of things in spite of myself on forums related to my job, and while it remains amateurish, I think you are confusing a lot of things.
First, Russia, as in the current Federation of Russia, is absolutely not USSR or Warsaw Pact.
First we have to get back a bit in time, between the end of WW2 up to the 80s. USSR is a colossus that encompasses satellites states as far as DDR (which is already western Europe, or at least central). Its manpower is incredible and NATO perfectly knows that they are absolute masters on land: manpower, and especially armour and tanks that NATO cannot possibly match until the very late Cold War (just before the collapse), with the introduction of more modern gear actually able to stand against the soviet arsenal of T-72B, T-80B, etc, by introducing the modern lines of armour that we know (Abrams, Challenger, Leopard 2, etc). Before the middle of the 80s, USSR not only has a colossal amount of those, but they are far superior to everything that NATO can field (NATO strengths rely elsewhere). Due to that state of affairs, NATO was incredibly under pressure from West Germany in particular, but also all the NATO Europe that knew that a single, head front massive assault from their soviet enemy would just pierce through anything like through butter. That is incidentally why they started to setup in the
Fulda Gap in part as a way to counter that.
Now then, before I start rambling, my point is that Russia is not that USSR. Russia hasn't the steamrolling capability that USSR held.
Second, just add up the countries that you showed on your pic : approximately 900 tanks, and 1500 IFVs for the 3 allied countries depicted. That is indeed a bit less than what Russia fields. Now then, add Italia, Spain, Poland, etc. I am pretty sure we can come to a respectable amount of forces that would be a match for the Russian numbers depicted. Moreover, I would put my money on a defending army at equal numbers, even if slightly less.
I actually think that what could make Russia win in such a case scenario is that UK, France and Germany forces are already spread thin all over the globe.
I also think that while indeed Lybia showed that European militaries had to rely too much on specific hardware and force projecting tools that the US lent them, it doesn't mean that they can't do it without them. Proof is currently, France is doing perfectly fine on its own in Mali, Center Africa, and Iraq. They were just happy to rely on the US because the logistics are not great (yes, they do not have the sheer capabilities the US have) and extremely expensive.