In "The Garden Party," what do the hats symbolize?
Excellent observation. I think you are right about the way in which hats are used to reinforce class distinctions, which is of course such a massive theme in this short story as a whole. However, in my opinion, the hat that is most important is the one that her mother cunningly uses to distract her daughter from her moral principles and to seduce her with vanity. Consider how the sight of herself in the mirror impacts her:
There, quite by chance, the first thing she saw was this charming girl in the mirror, in her black hat trimmed with gold daisies and a long black velvet ribbon. Never had she imagined she could look like that. Is mother right? she thought. And now she hoped her mother was right. Am I being extravagant? Perhaps it was extravagant. Just for a moment she had another glimpse of that poor woman and those little children and the body being carried into the house. But it all seemed blurred, unreal, like a picture in the newspaper.
Vanity, as symbolised in the hat, is shown to be such a powerful force that it distracts Laura and makes the very strong impression she had of the suffering of the Scotts become "blurred, unreal, like a picture in the newspaper." It is this that is the most significant usage of hats in the story, as it is the means by which Laura forgets her sympathy temporarily and also points towards her maturing and developing as an adult.