Blizzard's Kaivax posted "Coming soon to the Beta" on September 23 with a video showing heavier rain and fog in Elwynn Forest. The post confirms an upcoming weather-effects change, but does not name a date, patch number, complete zone list, or player toggle.
PC Gamer's report describes the rollout as covering certain beta zones and highlights the Goldshire downpour. The same report says snowstorms, sandstorms, and other weather types may arrive later, so the teaser should not be read as confirmation of a full weather overhaul yet.
This is a small but meaningful beta quality-of-life signal. Forever's world is one of its strongest draws, and stronger storms would add the visual density and reduced visibility associated with older WoW versions. The next check is the full weekly update expected on September 24.
SOURCES: Kaivax's official forum post, Blizzard's weather video, PC Gamer coverage, and Wowhead's indexed report.