The second tale of Conan Howard penned, the first "original" actually as The Phoenix on the Sword started out as a Kull tale and was reworked, is The Frost Giant's Daughter. Ironically, this tale didn't sell, so a few years later Howard renamed the character Amra (an alias of Conan) and had it published in a fan magazine.
The story is that of a very young Conan. It doesn't say how old he is, but I'm guessing he's still a teen, maybe 15 or 16 in the story. He's battling with a group of Aesir against the Vanir, north of the Cimmerian border. The story starts with him the last survivor of an ambush, against the last survivor of the ambushers. Of course Conan wins, and as he sinks into the snow in exhaustion, a nearly naked and extremely beautiful woman appears before him.
She taunts the barbarian, and his lust awakes him and gives him the vigor he needs to chase her across the arctic barrens. It's a variation on the Atalanta myth, and I can see a few possible reasons why Howard wasn't able to sell the story.
First of all, Conan is basically a slave to his raging hormones. It could be argued that Atali, the Frost Giant's Daughter has enchanted him, but it seems from Howard's prose that it's more that Conan wants to bang her, and he's stubbornly pursuing her of his own accord for that purpose. Of course, Atali wants Conan to follow her into a trap of her own, and when Conan quite handily vanquishes her two frost giant brothers with about three or four sword strokes (try doing that in D&D!), and begins catching up to her, she panics and uses supernatural means to escape the lustful "hero." Conan is presented as just another horny teenage boy, really, although one who's already larger, stronger, and more skilled with a sword than most other men. It's not the most flattering picture of the hero.
Secondly, the overt sexual nature of the story fits in with a lot of rape myths, but may have been too strong for the publishers of Howard's day. The Pulps had plenty of sexualized stories, but this one may have been too blatant.
Still, on the positive side it does tell of an interesting supernatural event from Conan's youth, one that helps shape his personality later in life. Viewed in the context of the collection, it's a worthwhile story. On its own, it's a bit weak. There could be a really powerful psychological tale of a femme fatale who tempts the wrong man, who happens to then obsessively pursue her with the intent of rape. Howard, however, wasn't really that sort of writer, so instead we get a sort of interesting event from Conan's life, but not a really riveting one.