This Princess was the Ice Princess. She was frozen and Ash melted her with a fireball out of Princess's mouth. However, she died and her spirit flied to up as she dropped a tear of out her eye, which cured Ash's Princess, she could talk again and didn't do fireballs out of her mouth.
The Ice Princess was probably the daughter of the Ice Avatar, just like the Light Princess is the daughter of the Light Avatar. And aswell, like the Light Princess, the Ice Princess had probably a spirit form too.