Here are some tips for creating a fuzzy illuminated scarf with color-changing LEDs, with a relatively simple process that is suitable for someone with limited sewing or soldering experience.
The lens of each of these RGB LEDs contains its own red, green, and blue emitters, and a built-in processor to make it blink or fade between colors, so you can achieve a fairly sophisticated effect with a simple circuit, and no external driver. The flexible connecting wires are concealed by a fabric lining, so the finished product is very comfortable and easy to wear. The lights create a nice diffused glow in the fur - wear it as a conversation piece, fashion statement, or safety accessory.
The number of lights in the design can be scaled up or down, with no need for a current-limiting resistor, although battery life will decrease as you increase the number of lights (unless you upgrade to a larger 4.5V supply).