"Winter" comes to us from the Old English word "wintar" and perhaps Lithuanian 'vanduo' -- meaning water, and likely coming from the stormy, snowy time of the year.
"Spring" simply appears to have its origins as a time when plants "spring up" and old English "springan" which is "to leap and burst forth."
"Summer" comes from the Old English word "Sumor" which meant the "hot season of the year."
"Autumn" is more difficult. It came from the Latin word "Autumnus." The Elizabethans than casually used "fall" around the 16th Century to denote it as the time when the leaves fall. Both terms were brought to America when the English colonized it, but fall eventually won out here, while "autumn" is still the word of choice in England.
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