Icy's name describes both her literal powers and her personality: cold-hearted. She hasn't a nice bone in her body; while she does want to rule the universe, she is also mean just for the sake of being mean: she gets kicks out of it.
Icy is the unofficial leader of the Trix sisters, though she is often willing to hand down that title when it suits the Trio's desires, or suits her own needs. She is easily the most determined of her sisters, most willing to do absolutely everything to get what she wants, though she is not quite as calm and collected as Darcy.
Icy has a baby duck that stalks her. However much abuse she shows the duck, it still keeps coming back for its "mama."