Random textures simply don't apply to minecarts.

I tried changing the texture of the minecart base and when I'd place one down it would only have the default texture.

What's weirder is I changed the texture of a chest, which worked when placed in world, but the texture of the chest in the chest minecart didn't change.

There is no chest minecart texture, the game uses a combination of both normal minecarts and normal chests

I should note this is fabric V3.1.2 for minecraft 1.19

at the moment minecarts are not yet implimented, they will be in an update soon