I get the feeling you've put a lot of prior thought into this anon. :P Oh well I'm enjoying my self
Katara is mostly water and ice
Piplup ending on Empoleon is a no brainer with her being from the southern water tribe.
Froslass is probably the closest thing to her Painted Lady of the lake
Poliwag seems like a fun choice she could share with her brother where he goes for Poliwrath and her for Politoed
Pelipper for rain set up
Abomasnow for snow
Lapras for surf and I like the idea she has one Pokemon that struggles on land.