Artist Claire Hummel describes Elsa's outfit:
"Frozen is purportedly set in the 1830s-40s, but I've been obsessed with finding a style that could marry her coronation gown with her ice gown more seamlessly; the open robes you see during the Regency era, including those being worn by Scandinavian royalty at the time, seemed a particularly apt analog for he weird underarm-cape thing. You also see her mom wearing something very similar for something like 10 years, so it's not a huge stretch to think it could be a popular look in Arendelle."
When designing Rapunzel from Tangled (which is in a fantasy time period/setting), Claire took some liberties. She notes, "I ended up going with the late Regency. There are a ton of gowns circa 1820 that have those inimitably princessy sleeves, and those palace guards aren't fooling anyone."
Mulan's setting is complicated due to "the original legend taking place in the Wei Dynasty, the Huns as an actual threat during the Western Han Dynasty, the Forbidden City of the Ming Dynasty, and the hanfu fashion setting it earlier." So instead of putting her in a specific period, she just used "plausible historical textiles and hanfu."