A song is whatever you want it to be. Its all a matter of opinion.
The same way that you could say that a song isn't a "summer song" or a "love song" could remind you, or bring you back to a point that makes you associate with that time period. It may not be a christmas song, but if you played it all season this year, and then played it in 4 months, it'd probably evolve into a christmas song in your mind. Feel me?
So No, but... Yes.