It doesn't learn Ice Beam by level up. It can learn it by TM13 in all generations though.
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dragonair can learn ice beam any level
Lapras will learn Ice Beam at level 31.
yes, it learns ice beam at level 35
No level. A Quagsire can't learn Ice Beam by normally training. You can however, buy Ice Beam at the major store/mall in the game (Depending on what game you're playing).
The only way Empoleon can learn Ice Beam is to buy the Tm from the Veilstone Game Corner