While rainbows in dreams usually represent our future plans and hopes, their significance completely depends on their color and even what you felt when seeing it in your dream. As per Dream Astro Meanings, a classic, colorful rainbow means major good luck is on the horizon, especially if you felt "calm, confident and serene" when looking at it. However, that is not always the case.
If you saw a fading rainbow in your dream, it might mean your dreams will not come true just yet. But not to fret — seeing a rainbow in the first place means it probably will happen, it will just take more time and patience. Fading rainbows can also symbolize living in the present moment and appreciating your life's joys today before they disappear (via Dream Astro Meanings). Similarly, a gray rainbow may mean your "pot of gold" might take more time to reach, but should give you the necessary push to work even harder toward your goal (via Astrology Answers).
A totally white rainbow is the ultimate symbol of purity and spirituality, and symbolizes a time of peace, rest, and tranquility (via My Dream Symbolism). As per Astrology Answers, an elusive white rainbow may even mean a connection to higher spiritual powers, or a message of love, joy, and happiness.