there is no minimum age for a character, but it's usually recommended to be above 12. that said, your character could have tricked their way into the group, or followed them until they couldn't turn back. 

as for the power, it wouldn't be called magic, it would be called Cryokinesis, or the ability to control ice. That said, Cryokinesis alone is pretty flimsy for this RP, so i would recommend at least expanding it to Thermokinesis, or the ability to control temperature.