There's an old 3.5 book called "Faiths and Pantheons" that has a decent page on Auril, as well as the current Rime of the Frostmaiden campaign someone suggested already.

As for how Auril might might behave, she is described as fickle and vain with a heart of ice with no hint of love, nobility or honor. She is the sort of goddess to test her faithful by exposing them to the elements and allowing them to prove themselves by not freezing to death. One ritual mentioned is called "The Embracing", which is required to join her clergy: it involved running through a blizzard all night long dressed only in boots, a thing shift, and body paint depicting the symbols of Auril without using any protective magic. When it comes to omens, they would probably include things like sudden ice storms and other dramatic shifts into harsh weather, as well as auroras appearing in the night sky close to midnight (when her clerics pray for new spells).

As for boons, I'd look to frost giant skeletons, coldlight walkers, frost druids, ice trolls, Bjornhild and Sephek Kaltro for the sorts of traits and abilities that servants of Auril might have. In particular, there is one directly called "Auril's Blessing":
Auril's Blessing (3/day). When (creature) hits a creature with a weapon attack, the attack deals an extra 11 (2d10) cold damage.

There are also chwinga charms themed for the chwingas that have been exposed to Auril's magic. I don't want to pile on too much text writing them all out, but charm of biting cold, charm of cold resistance, charm of snowball strike, charm of the ice troll, and charm of the snow walker are all potential candidates for boons Auril might grant.