So they're just an intrinsic property of each character rather than something meaningful. I guess that makes sense
The colours affect certain roles.
Gideon cares about white planeswalkers and Nissa cares about green planeswalkers, but they're not in the game.
And Tamiyo/Narset/Ugin reveal the target's colours, which helps you identify their role. This is important because all white walkers, except Sorin, can't be mafia.
(In spoiler-rules)
The following planeswalkers (roles) will not be mafia: Ajani, Gideon, Elspeth, Nahiri, Venser, Narset
Kicker: Sorin's not in the game, making all white planeswalkers you find instantly confirmed civvies.