Is this true about weather?

No. The weather is affected by many things. If one tried to base seasonal outlooks on that philosophy, they would bust the vast majority of the time. Things like El Nino Southern Oscillation, Pacific Decadal Oscillation, North Atlantic Oscillation, Arctic Oscillation, atmospheric blocking, where polar vortices set up, solar activity (minimums and maximums), are but some of the things that affect the weather.