You would be correct with spring and summer. Spring is haru (when hanami occurs hence the pink), summer is natsu, autumn/fall is aki and winter is fuyu. The group could be known as the Shinobi no Shiki (Ninja of the Four Seasons).
Spring should be strawberry blonde (pink hair) and Autumn/Fall should be a ginger. As for the Pokémon, a big factor would be the size of their parties. Appearing to be field minions similar to the Hexagon Brothers (from Pokémon XD) or lieutenants like the Shadow Triad (from the Gen-V games) their teams would probably consist of no more than four Pokémon; each one with a Sawsbuck headliner to fit the season theme. With that in mind, my suggestions are as follows:
Spring would mainly specialise in Grass-type Pokémon with an affinity for Bug and Fairy types so their team would probably consist of Shiinotic, Accelgor, Sceptile and Sawsbuck (Spring Form).
Summer would mainly go for Fire-type Pokémon so their team could consist of Salazzle, Centiskorch, Pyroar (female) and Sawsbuck (Summer Form).
Autumn/Fall would specialise in Ghost-type Pokémon so their team could consist of Gengar, Decidueye, Dragapult and Sawsbuck (Autumn Form).
Winter would obviously specialise in Ice-type Pokémon so their team could consist of Weavile, Glaceon, Alolan Ninetales and Sawsbuck (Winter Form).
"You're right, Chuck," Shiranui replied, "Get your strongest Pokémon healed up and ready 'cause our next stop is the Altar of the Sunne and Moone and places unknown."