lovely weather for a skate glide together with you

Quick: for the pleasure of being absolutely correct, what have they just sung?
— "You say tomato, I say tomato"
— Let's Call the Whole Thing Off 
— I've Got  My Love to Keep Me Warm
— Shall We Dance (Gershwin & Gershwin))
— Shall We Dance (Rodgers & Hammerstein) 
— They Can't Take That Away from Me 
For extra credit which if any won the Academy Award for best song of the year? Three were eligible.