Resembling a frog, or hoarse and croaky like a frog's voice.
From 'frog' (from Old English 'frogga', onomatopoetic—the sound of croaking) plus '-y' suffix meaning 'like or full of.' Simple descriptive formation.
Froggy is pure onomatopoeia hidden inside—'frog' came from the sound frogs make, so calling someone's voice 'froggy' is just comparing one croak sound to another! English absorbed the frog's actual noise into the animal's name.
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