It’s actually arguable whether in the Disney animated feature Snow and the Prince are meeting for the first time at the well. In “I’m Wishing,” Snow sings that she’s “wishing for the one I love to find me today.” It’s ambiguous, but it suggests that there’s already someone she loves–not that she’ll meet someone she CAN love.
His first words to her (all in song) are “Now that I’ve found you, hear what I have to say.” That can be read two ways: He’s just met her, OR he’s been looking for her for some time. Since the Queen forced her to dress in rags and act as a servant, it may be that she suddenly vanished from the royal scene, leaving the Prince searching for the girl he’d already fallen for.
It certainly CAN be read as love at first sight, but that’s not the only possible reading of their encounter at the well. Cinderella and Ariel are more guilty of this than most of the other Official Princesses. (And of course it’s a long-standing cinematic trope for two characters to meet, fall in love, and presumably/actually marry within the 90 or so minutes of a film–which necessarily shortens the relationship for the viewer even if a longer time is represented.)
Keeper of Belle's Gold magic, sand dollar, cloaks, purple FTL outfit, spell scroll, library key, copy of Romeo and Juliet, and cry-muffling pillow, Rumple's doll, overcoat, and strength, and The Timeline. My spreadsheet: https://drive.google.com/file/d/0B6r8CySCCWd9R0RUNm4xR3RhMEU/view?usp=sharing