I doubt he could freeze Superman's insides. His innards are protected as well as his outer body (how else can he suck in poisoned gas, etc. and just spit it back out?).
Also, Lord Fear is right:
Superman's physiology differs from humans, it is unknown by how much because current technology isn't able to see inside his body. However, when he was injured by Gog in Action, he was taken to STAR labs...and the Kryptonite in his body enabled the doctors to see inside of him...at least a little bit.
So far (besides the two organs in his body that produce his special powers):
His appendix is a fully formed organ.
His resting heart-rate is near stopped.
His body temp is slightly elevated.
His blood pressure is nonexistent.
So I'm sure Superman could use his heat vision to melt Iceman, but he can't permanently take him out unless Iceman reforms enough to be flown into space.
Iceman, on the other hand, can't do anything to Superman. That moisture inversion stuff won't do anything to him, his forcefield will protect him. Freezing/ice won't hurt him: he's been in the depths of space...and until recently his hideout was in one of the coldest places on Earth. Superman is no stranger to cold temps.
It's a stalemate at best, a win for Supes at worst.