Certainly, the MSR StormKing ($799) is a possibility. It's a four- to five-person tent, meaning it'll squeeze five people in at a pinch. As you correctly note, that's 12 square feet per person for a party of five. Remember, though, the dog could sleep in the vestibule, it's a well-made tent, and its weight (15 pounds) is competitive on a per-person basis with just about any tent out there.
One alternative is Sierra Design's new Nomad ($449), which is more in the range of 13 to 14 square feet per person, and is designed as a true five-person tent (people sleep in alternate directions, three with their heads north, two with heads south). It's heavier than the StormKing (20 pounds), but that's still not bad if you spread the load among the group. It also boasts two vestibules for storage. While it's billed as a three-season tent, this may be to your advantage. It's plenty sturdy for wind and snowy conditions, so long as the tent is thoroughly staked out and you pitch in as sheltered a location as possible. As a three-season tent, it also has more ventilation than true winter tents. With five people and a dog exhaling their water-laden breath all night, this may help keep condensation down to tolerable levels. It's worth a look.
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