Of course NATO is a threat, or at least it is credibly perceived as one in Moscow. Do you think the US would tolerate the Warsaw pact on its own borders merely because it has nuclear weapons? (Cuba knows the answer to this question, the US does not).

There's plenty of examples like the deployment of missile defenses to Eastern Europe (which contrary to the name is strategically an aggressive move, as they're first strike enablers, diminishing strategic deterrents. The one thing Russia is supposed to rely on). The basic point is, no country on earth has stopped deploying its military in the pursuit of national security merely because it is a nuclear power.