Where does the magic the Ice Queen evokes come from?
The Ice Queen's magic was a dark magic that came from her original world and existed before time began (prehistory of the prehistory of Narnia). In the magicians nephew, it spells out how she invoked an evil based on hatred, and it consumed her entire world, herself included. It was only by accident that Digby (the Professor in LW&W) and Polly awoke her (she serves as the metaphor of Satan, imprisioned in hell but released to devour whom he may consume).
The staff she uses in LW&W came from her original world, which she had turned completely into stone, including herself - when Edmund destroys her staff he also destroys her ability to conduct magic on Narnia.
This is the epic turning point in the battle, and the difference between the magic of Potter and of Narnia. Even death could not stop the true God, and the battle was won, not with magic, but with the resurrection of the once thought dead God entering the battlefield along with the resurrected saints.
Potter is just a tired repeating cliche of "good" sorcerer performing "good" magic vs evil sorcercers and witchs performing evil magic - and everyone acting on thier own impulses because they have no moral base identified.
She is from another world, Charn. She is not human at all, but a descendant of a djinn and a giantess (Lilith, in fact . . . Adam's reputed first wife.) So of course she has a giant's strength and a djinn's magical powers.
She was brought into Narnia by Digory Kirke . . . and this indirectly resulted in the wardrobe, as you can read in The Magician's Nephew.
"It's all in Plato, all in Plato . . . bless me, what DO they teach them in these schools?"