It actually makes a lot of sense, if you think about it. Since Arctozolt is formed from two separate Pokémon, it stands to reason that each one would have had their own move set originally, which were combined to form the moveset of Arctozolt. Since the fists of Arctozolt come from the "Zolt" half, there's no reason for it to learn Ice Punch, especially since the the "Arcto" half probably couldn't use Ice Punch either, as it likely had fins instead of fists. Basically, neither of the component halves would be able to use Ice Punch themselves, so the combined version shouldn't be able to either.
It's little details like this that show that Game Freak doesn't just slap moves on to a Pokémon willy-nilly. They come up with logic and reasons behind every move (for the most part).
I'd say the Zolt part on it's own should be be able to learn it. I'd say it was a bit more of a natural ice punch user than say Wooper or Gulpin.