I doesn't work that way. You need to mix two of the "school" pets that you get at level 48, or mix with a retired promotional pet, if you want a hybrid. Even then you might just get a repeat of your own pet.
You can't hatch an icebird. I have one, however, and you can win it from Nightwing in GH. He's a hidden boss in Ravenscar, on the frozen wasteland (or something like that). It's not too rare of a drop... the hardest part is working your way up to Ravenscar in the first place. I hope this helped! Good luck! 8)
