Glalie
Possible nicknames: Zorro, SoccerFace, Jawbreaker
– Ice Beam
– Crunch
– Hail/Sheer Cold
– Shadow Ball/Water Pulse/Earthquake/Blizzard
Glalie is, personally, one of my favourite Pokémon aesthetically. Unfortunately, it's stats are only so-so. 80 across the board isn't bad, but also not as good as other Ice Pokémon. For in-game purposes, those stats should be fine. especially because you'll likely be using Glalie to fight the Dragons who are 4x weak to Ice. For non-Ice attacks it gets some nice coverage moves, but most of them from TMs.
Verdict: A decent choice. Not outstanding in any area, but also not terrible. Learns good coverage moves but mostly via HMs. Possible bias on my part because Glalie is amazing.
Walrein
Possible nicknames: Reinhardt, Tusken, MuttonChop
– Blizzard/Ice Beam/Aurora Beam
– Surf
– Waterfall/Dive
– Hail/Body Slam/Strength/Rock Smash
Walrein is a better choice than Glalie due to its bulk and better Sp. Attack. However, it stacks weaknesses with Swampert, is slower, and doesn't learn Ice Beam naturally. Walrein does get access to lots of HMs. It is also quite bulky.
Verdict: A good choice if you're willing to sacrifice your Ice Beam TM. Stacks a Grass weakness with Swampert. Can learn a lot of HMs.
Regice
Possible nicknames: Prism, Titanic, Jotunheim
– Ice Beam/Icy Wind/Blizzard
– Thunderbolt/Shock Wave/Zap Cannon
– AncientPower
– Lock-On/Strength/Rock Smash
Stat-wise, Regice is the tankiest of the Ice-types in Emerald. Like Walrein, however, it requires TMs to learn good moves, including Ice Beam. It does get Electric and Rock coverage moves and the highest Sp. Attack of the three, as well as Lock On + Blizzard/Zap Cannon if you don't want to use your Ice Beam TM. Regice can be a chore to get, however, and is also a Legendary, which you may not like using.
Verdict: The best option. Requires the Ice Beam TM. You may not want to use it because it is a Legendary. Regice is slow.
Gyarados
Possible nicknames: Oroboros, DangerSnek, Leviathan
– Ice Beam
– Surf
– Flamethrower/Fire Blast
– Earthquake/Bite/Thunderbolt
Gyarados is the only non-Ice type Pokémon I feel is worth mentioning because, unlike other Water-types, it does not share weaknesses with Swampert and actually benefits from Swampert's Ground typing. It needs to learn Ice Beam by TM, but it gets lots of other fantastic coverage moves, as well as Intimidate. Plus Gyarados makes any playthrough like 100x easier.
Conclusion:
Regice is the best Ice-type in Emerald, with the highest Sp. Attack stat, good bulk and a diverse movepool. If Regice isn't your thing, I suggest Glalie due to its balanced stats and good movepool, as well as not needing a TM to learn Ice Beam. Walrein is the worst if you also have a Swampert due to weakness stacking, but it can be used as an HM slave to give Swampert room to use more coverage moves. Gyarados is an option if you're willing to sacrifice your Ice Beam TM in return for a terrific Pokémon with amazing coverage.
