As you can see, if you are truly ice, you will receive the quest to get the Ice Guardian spell at level 28. You will not receive the quest for the Animate spell, that is a Death School spell and you will not be able to train it, however you may be lucky enough to find it on an item or as a Treasure Card.
If you want the prize, you have to build the ladder rung by rung. There are no shortcuts.
The Ianthine Spectre pet gives the Animate card at birth. You can buy this in the Crowns Shop for 9880 Crowns. It's said that the Gurtok Demon also drops this pet very rarely (I've heard of people not getting it after hundreds of tries, while others get it after a few tries). Being a Crowns drop, the chance of getting it is much smaller than of getting a non-Crowns drop.
One point about the Animate spell. Since wizards can only have 7 pip placings at one time, and since power pips are used as single pips for spells outside of the primary school, it means that the largest minion a non-Death wizard can cast is the 7-pip Living Scarecrow with 700 health. The pet is probably not restricted this way, but it's not likely that a pet will wait until it has 7 power pips before casting Animate.
I have no idea which enemies drop the card. I know that the Marvelous Minions treasure card (Crowns) pack has one very infrequently. The card can sometimes be bought at the Bazaar, but I've only rarely seen it there.