I'm not so sure about that. Here's the results of /nds water, !ice beam
Magikarp (limited movepool)
Rotom-Wash (water-type by technicality)
Tympole
Palpitoad
Seismitoad
Keldeo
Skrelp
Volcanion (part fire)
Wimpod (sort of limited movepool?)
Pyukumuku (limited movepool)
Sobble
Drizzile
Chewtle
Arrokuda
Barraskewda
Dracovish
What makes it even more confusing is that besides the four understandable ones and Wimpod, all of these Pokemon learn at least one Ice-type attack, be it Ice Punch, Icy Wind, Ice Fang, or Ice Shard.
Things get much more confusing when you look at Ice-types that can't learn Ice Beam. There are exactly four:
Sandshrew-Alola
Sandslash-Alola
Rotom-Frost
Snom
Snom and Rotom make sense, as the former has a limited movepool, while the latter is only Ice-type by technicality. But why the hell doesn't the Alolan Sandshrew line learn Ice Beam?