If your campaign is set in the Temperate Zone, remember that the area doesn't really have it's own weather: it's always importing Someone Else's weather.
This Someone Else's Weather is brought in through Fronts. Think of Battle Fronts, because that's where the idea of weather fronts comes from.
A warm front comes up from the southwest or south or rarely, from the southeast. A cold front comes from the west or northwest, but can come from the north, northeast, or even southwest (chasing the warm front.) A warm front brings temperatures warmer than normal for the area, the cold front brings temperatures colder than normal for the area, and everyone grumbles constantly about it being either too hot or too cold.
This push and pull of fronts is endless and inexorable and most annoying. Winds howl and roar from the south after a warm front passes, then howl even faster after the cold front passes. Great soaking rains occur ahead of the warm front, then severe thunderstorms occur ahead of the cold front. After the cold front passes, grey skies and drizzle are followed by cold clear nights.
In the winter, rain (or worse, icestorms) and rain and snow occur north of the warm front, rain occurs ahead of the cold front, and arctic blasts follow the cold front. If the area is north of the low pressure center (where the warm front and cold front start) then a snow storm occurs.
Low pressure centers are the places where, as noted, cold fronts and warm fronts start and extend away. Think of them as anchors.
Where do low pressure centers go?
This is dictated by roaring winds aloft known as the jet stream. The jet stream carries low pressure centers along it, slowly in the summer, and swiftly in the winter. The jet stream is further north in the summer, further south in the winter. And the warm air is warmer, the cold air less cold, in the summer. In winter, the warm air is less warm ('hey, it's up to 0 Celsius! How nice!') and the cold air much colder.
In Lexington, Kentucky, a typical temperate climate occurs. Here are averages for that area:
January: highs in the 30s, lows in the 20s, average (varies greatly)
February: highs in the 30s, lows in the 20s, average (varies greatly)
March: highs in the 40s, lows in the 20s, average (varies greatly)
April: highs in the 60s, lows in the 40s, average (varies considerably)
May: highs in the 70s, lows in the 50s, average (varies some)
June: highs in the 80s, lows in the 60s, average (varies little)
July: highs in the 90s, lows in the 70s, average (varies little)
August: highs in the 90s, lows in the 70s, average (varies little)
September: highs in the 80s, lows in the 60s, average (varies some)
October: highs in the 70s, lows in the 50s, average (varies considerably)
November: highs in the 60s, lows in the 40s, average (varies greatly)
December: highs in the 40s, lows in the 20s, average (varies greatly)
In Minneapolis, a harsh temperate climate occurs:
January: highs in the 1s, lows in the -10s, average (varies tremendously)
February: highs in the 1s, lows in the -10s, average (varies tremendously)
March: highs in the 20s, lows in the 1s, average (varies tremendously)
April: highs in the 40s, lows in the 20s, average (varies greatly)
May: highs in the 60s, lows in the 40s, average (varies greatly)
June: highs in the 80s, lows in the 60s, average (varies considerably)
July: highs in the 80s, lows in the 60s, average (varies considerably)
August: highs in the 80s, lows in the 60s, average (varies considerably)
September: highs in the 70s, lows in the 50s, average (varies greatly)
October: highs in the 50s, lows in the 30s, average (varies greatly)
November: highs in the 30s, lows in the 10s, average (varies greatly)
December: highs in the 10s, lows in the -1s, average (varies tremendously)
In Atlanta, a warm temperate climate exists:
January: highs in the 50s, lows in the 30s, average (varies greatly)
February: highs in the 50s, lows in the 30ss, average (varies greatly)
March: highs in the 60s, lows in the 40s, average (varies greatly)
April: highs in the 70s, lows in the 50s, average (varies considerably)
May: highs in the 80s, lows in the 60s, average (varies slightly)
June: highs in the 90s, lows in the 70s, average (little variation)
July: highs in the 90s, lows in the 70s, average (little variation)
August: highs in the 90s, lows in the 70s, average (little variation)
September: highs in the 80s, lows in the 60s, average (varies slightly)
October: highs in the 70s, lows in the 50s, average (varies considerably)
November: highs in the 60s, lows in the 40s, average (varies considerably)
December: highs in the 50s, lows in the 30s, average (varies greatly)