Hi!
A unicorn/alicorn's magic CAN change! Yes, it's true!
In Season 1/2, Twilight's magic was a baby-pink/white color, and it was seen first in the two opening episodes of Season 1 of My Little Pony, Friendship is Magic. In season 3-6, however, her magic had turned hot-pink Weird, right?
In Season 1, Rarity's magic was the same color as Twilight's at the time - baby pink. You will notice this when Rarity cuts off her tail in part 2 of Mare in the Moon.
In Season 1 or 2, Celestia's magic was the same color. In season 2/3, it turned yellow to match her cutie mark, the eight-pointed-sun on her flank.
Princess Luna's magic changes too! Crazy, right? In Season 1, episode 2, in her Nightmare Moon stage, her magic was a neon-blue/turquoise color. After this, when her mane changed from a regular flat one to her wavy kind, her magic turned the same color as her eye shadow.
That's not all, though! I see some posts about Cadence/Princess Mi Amore Cadenza's magic turned from blue to green, when in reality, Cadence's magic never changed. You should realize the Cadence with green magic was a fake. LOL
And last but not least, DJ PON3's magic changes. Her magic color used to be a baby-pink, but in season 4 it turned darker, like Twilight's in season 3.
That's all for now! I hope you enjoyed and liked my "story"!