In this war we have already been primed and aligned. Europe has been effectively aligned with Ukraine, whether it was through propaganda or plain high quality media coverage. So at the very least we will be sad to see Ukraine fall. On top of that we have been thoroughly informed that Russia is a threat to the EU, and Russia has done nothing but confirm that belief.
Besides being selfish we are self preserving. And we'd rather be cold and dropped down a couple notches economically, than have our entire union be threatened by some kleptocracy.
Most people would probably be ok with passively waiting for Ukraine to fall, and being cold while doing so, as well as reinstating relations with Russia after the war is over. But I think if EU leadership decides action is needed and we need a more active hand, it will receive majority support from the populace.