River Song was never nude. She might have appeared that way when she was wearing a strapless dress. The angle of the shot made her appear nude but she was in fact not.
Steven Moffat confirmed on Twitter that a scene involving a nude River Song was removed for being 'too naughty'.
Deleted, yes. Too naughty, don't know what I was thinking.
There was also a brief sequence with a group of Nazis. This was cut out for time. For the record, both scenes were to have appeared in "The Impossible Astronaut". River was to take her clothes off in order to seduce her way out of prison after receiving the Doctor's letter.