The Dungeon Master’s Guide generates weather with three quick d20 rolls — one each for temperature, wind, and precipitation. Most results are normal for the season and region; the high rolls produce the memorable extremes that actually affect play.
A hot or cold roll shifts the temperature by 1d4×10 °F. Extreme heat (above 100 °F) or extreme cold (below 0 °F) forces a Constitution saving throw roughly every hour or a level of exhaustion. Strong wind imposes disadvantage on ranged attacks and on Perception checks that rely on hearing.
Heavy precipitation and fog create a lightly-to-heavily obscured area — disadvantage on sight-based Perception and trouble with ranged attacks. Roll weather to add texture and the occasional real obstacle to overland travel, from a slowing blizzard to fog that hides an ambush.