The players can be customised with different body part colours, but there's no option to use textures.
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Instead of textures, a simpler option will be for decorations or accessories. For example, characters can wear badges, ties, logos on their bodies; hats, headgear and hairstyles for heads; shoes and so on.
Another option is to have different "outfits" that still have coloured regions. For example, the current "outfit" is a different colour for arms, body and legs. A "telnyashka" (Russian sailor shirt) outfit could have a leg colour plus two colours used by both the arms and body in a striped pattern. A tuxedo outfit could have a single colour for most of the arms, body and legs, a second colour for the shirt, and a third for the shoes.