A scythe is a tool for harvesting grain, which is about as representative of changing seasons as a weapon can get. It conveniently also resembles the crescent moon, which fits the Druid motif, and is one of the oldest lore weapons in WoW, dating back to the Vanilla Duskwood quests IIRC.
The association with death is a much later advent that is just a play off its symbolism for the harvest.