I don't have the score in front of me so I will refer to points in the song by approx time.
"Colour" in music is a difficult way to describe works. In a way a composer from the romantic era paints an idea using notes. In this way Tchaicovsky uses the high woodwind and strings to paint a picture using sound. As for what colours, well the term colour in music is a synonym for timbre (other spellings - tambre or timber) which is the quality of the sound.
So if you want to know the quality of the sound (and I don't mean good or bad), the answer is to listen and identify how the composer is orchestrating his work. For example, in this, the high woodwind give a bright colour to the music, while the short articulation and rhythm give a light, bouncey feel to the piece. This is supported by the lack of long bass notes that would counter the effect of the high and short woodwind and strings.
The piece starts graceful and light, and Tchaikovsky's instrumentation is how he achieves this. The flutes and violins make use of short detatched notes in the upper register to avoid any broad sounds though this technique is more noticable in the lower strings that use detached notes to avoid the depth and warmth that comes with long notes on the cellos and double basses.
About 1:30 in, the mood changes and the higher brass (previously absent) bring a warmth, supported by the longer notes in ostinato in the deeper brass. This is supported by a simutanious change to a minor key and together for the next 30 sec or so provides a darker and deeper contrast to the previous motif.
At around 2:00 (will change based on which recording you listen to), the piece returns to the light and graceful origins with a slight flamboyant flair at the end with the use of the timpani and a short cymbal "splash".
I hope this gives you some help for your assignment/paper.