The happy birthday song has actually been copyrighted until the year 2030.
But really no one is gonna get you into trouble for singing the Happy Birthday song because the people who own the copyright to the song are unlikely to be at your birthday party and people at your birthday part are unlikely to turn you in for singing the happy birthday son.
The happy birthday song has been sung at many birthday parties for many years without any problems.
So although it's copyright infringement you'll likely be okay singing it.
But if you put a video of the birthday party online such as Youtube with the happy birthday song being sung in it then it might get removed for copyright infringement,
Other than that nothing should happen.