I guess I'll start off by saying I've role-played for over 10 years, and have done the rounds. I've done it off and on, never to real super seriousness, (although I can!) I've been losing interest in it though sadly and have been getting on with IRL, which has taken a lot of my time up.
Icy is a cold gryphon, what a surprise, think of a phoenix but on the negative spectrum, phoenixes of fire are symbols of rebirth, so Icy here, is the opposite, taking lives, relishing in the death of all things. So the gryphon usually wills herself as a "Reaper" sort of role, playing with life and death how she sees fit. (I knooooow, fuckin EDGY rite)
As cringe as it is to say, she does have some pretty breakneck powers, the command of cold and ice, sapping the life and warmth from nearly anything she comes across. I know overpowered characters aren't very fun, (I respect that), so any approaches on your part will have to accept that this character is capable of such. Though I could maybe play her in a mortal setting, after all she doesn't use them -all- the time.
I've not been here in nearly a decade, wtf.