I’m not a competitive player, but I came up with this moveset for the story mode and I think it could work competitively.
Abomasnow @ Leftovers
Ability: Snow Warning
EVs: 252 Atk / 128 Def / 128 SpD
Adamant Nature
- Aurora Veil
- Stomping Tantrum
- Sheer Cold
- Ice Punch / Icicle Spear
Adamant is the best nature for the moveset because it doesn’t use special moves, so Atk is important but SpAtk is useless. Def and SpDef are also useful, since Abomasnow has more weaknesses than any other Pokémon.
Ideally, you would start with Aurora Veil. It only works in hail, which Snow Warning generates. Its defensive power makes up for the whole more-weaknesses-than-any-other-Pokémon thing.
Stomping Tantrum is Ground-type, so it covers most types Abomasnow is weak to, including its double-weakness, Fire. It has 75 base power, but it increases to a whopping 150 if the move is used after a failed move.
Sheer Cold is an OHKO move, which means it fails a lot. Alternating between Sheer Cold and Stomping Tantrum is a fairly effective strategy, especially with an Aurora Veil in place. (If Sheer Cold runs out of PP and the hail stops, you can always use Aurora Veil, which always fails outside of hail. That sentence had many rhymes.)
For the last move, go for Ice Punch or Icicle Spear. They’re both physical (benefit from Atk) and Ice-type (covers Flying-types, who are immune to Ground). Ice Punch can freeze and Icicle Spear deals high damage if it hits 4 or 5 times, so pick whichever you prefer.
This moveset also works for the story mode, especially since it only uses natural and TM moves.