If you go to the 'web' app or the 'wikihow' app on the phone, there should be a section that says 'How does the weather work?' That section should also explain seasons.
Basically;
-A sunny day gives +1 to ROCK
-A windy day gives +1 to SCISSORS
-A humid day gives +1 to PAPER
-Autumn gives +2 to ROCK cards
-Spring gives +2 to SCISSORS cards
-Winter gives +2 to PAPER cards
-Summer gives no buffs, it's like the neutral season.