Toadfrog, Horn players like the key of F--and standards like therse are always played in closed position. both for the rhythmic effect and to allow for a moving line to be played-- The F chord can be alternated with F6 and Fmaj7, and the C7 is alternated with Am7, so the first two lines would be played like this:

F/F6/Fmaj7/F6/
Am7/C7/F6/Fmaj7

Berlin actually did his writing in the Key of F#--