Hockey is by far the most popular winter sport, nothing comes close it, so no, it's not "just 1 out of many". Hockey actually has some stars that regular people heard about.
And what you are talking about isn't "social media". It's regular referendum. People didn't need any "influencing" in Budapest to vote against the Olympics, because they never wanted it in the first place, it's the most left-wing part of country where people are against most of the sport events. And as I said, there will always be some cities where the politicians in power will have the support of the public on this matter. Let's also not forget that not every country is a democracy. The Olympics doesn't need the Western democracies to host to survive.