A fun way to allow color to influence your character's choices is through the color of your character's clothing and possessions. When you build certain classes of characters within your RPGs, you immediately begin to envision certain colors being associate with those classes. Some examples might include:
Black, blue, and purple (Rogues)
White, gold, and silver (Clerics)
Green, brown, and orange (Druids)
But what is your character's favorite color doesn't fit within those stereotypes? Simple answer . . . screw stereotypes! Never be afraid to use the color of your character's clothes to help tell the story of who they are as individuals. There is something amazing about a swashbuckler rogue (e.g., Han Solo - Star Wars, Wesley or Enigo - Princess Bride, etc.) who loves wearing various shades of neon colors.
While clothing is something that your character will take with them everywhere they go, what about the color palette of your character's bedroom or home (if they have their own home apart from the group). Think about how your character's personal space is decorated and how their favorite colors are used within that space. Consider bed covers, drapes, paint on the walls, color of the carpet, color of pictures frames, and even the lighting source within the space (if your game allows for different colored room lighting).
Another way that you character's favorite color can influence the game's world is by letting your character be influenced or changed by various manifestations of those favorite colors. For example, does your character just like the color, or do that have an addiction to the color so much so that it could potentially have a negative affect on their life or the lives of their fellow adventurers? Does your character like the color purple just for their clothes, or do they put their entire team in mortal jeopardy because they absolutely have to mine the amethyst crystals they happen upon deep within the Underdark where the horde of Illithid dwell? Or maybe a curse has been placed on your character where anytime they see their favorite color they become very aroused by the person(s) wearing that color, regardless of your character's chosen sexual or gender identity.
Another possible way to introduce your character's favorite color(s) is in what certain spells, rituals, or various magics look like when they are cast. This is typically referred to as "flavoring" your spells.