No, the colours don't matter. Using red for positive and black for negative is just a convention. It helps everybody understand the way the circuit is wired, but the current will flow just the same whatever colour the insulation is.
Now, you may find it helpful to devise your own colour-coding scheme. Maybe inputs to the Arduino are blue, and outputs are orange, something like that. Anything that helps you keep the wiring clear and organised will help.
Non-working Arduino breadboard circuits are usually caused by a wiring error. Be sure that you understand where the breadboard holes are connected, and where they're not. If you can, get someone else to check your wiring, because it's very common to miss something if you check it yourself.