why doesn't eating snow quench thirst?

Snow does quench your thirst but because the water content is low it takes a lot of snow

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It melts down to less 'water' than you'd probably drink in one go.

I don't remember eating snow, it's kind of rare here in Florida.

But it could be that you miss the minerals when you eat snow. Most municipal and shallow well water is "hard", having substantial mineral content.  Snow is frozen precipitation and has no minerals. The only reason I can think of.

might be psychological, youre brain thinks you’ve not had any water because you haven’t physically drank water? Idk man just a guess