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).
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dragonair can learn ice beam any level
Lapras will learn Ice Beam at level 31.
It doesn't learn Ice Beam by level up. It can learn it by TM13 in all generations though.
yes, it learns ice beam at level 35
The only way Empoleon can learn Ice Beam is to buy the Tm from the Veilstone Game Corner