Colors play an important role in life -- psychologically, emotionally, and how-to-tell-when-food-has-gone-bad wise. And in the Zelda games this is no different. Except, well, you don't eat the fairies. Anyway, below are my theories on how their colors affect how they act.
Navi appears to be pure white with a bluish aura. The white inside could represent Navi's open-ness (she never hid anything from Link), and her pure-heart. The blue could represent her calm, caring attitude, her vast knowledge, and maybe even a tinge of sorrow from her past. Not a lot is known about Navi's past, and if she was trusted by the Great Deku Tree, something must have happened for her to prove herself, or earn his respect. Navi is also often the voice of reason and is constantly looking out for Link, although I'm not possitive if that's a trait for blue things. ^^;
I believe that Tatl is meant to act as an exact opposite of Tael, her brother. And since Tael is dark colored and follows the villain while Tatl is light colored and follows the hero, it makes sense. Anyway, Tatl is a pale yellow which is usually connected with meanings of joy, freedom, and awareness. And Tatl was certainly her own fairy. Despite her small stature, she has a spunky attitude and isn't afraid to say exactly what she's thinking, no matter how offending it is. However like most hard-outer-shell types, she is a bit of a softy on the inside, although don't expect her to show it often. She does have a reputation to uphold, and a younger brother to keep in line.
The fact that Tael follows Skullkid, the main villain in Majora's Mask and is also dark purple is hardly a coincidence. Dark purple is often connected to dark themes. For you Sailor Moon fans out there, you may recall that Sailor Saturn, the Scout of Destruction, had a color theme of dark purple. Her sailor outfit was dark purple, her attacks were dark purple, heck even her eyes were purple! Now although she wasn't evil, she was involved with evil people (well... actually those evil people lived inside her, but still). Switching to Legend of Zelda evidence, in Ocarina of Time the Shadow Medallion was dark purple, which as you know, was found in a graveyard. I don't know about you, but nothing spells spooky like a place for the dead. Also from that game, the Sheikah wore dark purple. They weren't "evil" per say, but a lot of unfortunate things did happen to them. In Majora's Mask, the evil mask itself was mostly colored purple. Dark purple is just bad news, color-wise. This doesn't mean that Tael was evil though, oh no. This just means that Tael was destined to follow the troubled dude.
Although the healing fairies have changed appearances over the years, the most interesting look was in Ocarina of Time and Majora's Mask. These pink-hued fairies could be found everywhere, and although they lacked individual personalities, they were always ready to refill Link's hearts. The color pink is often connected with feelings of love, beauty, tenderness, and tranquility. Valentine's Day is full of pink, stereotypical nurse outfits are pinkish, and some prison rooms are pink to reduce in-mate aggression. It's the perfect color to help a warrior enjoy a moment's peace.