Great question — answering as the UphillTech team:
During the time of adoption, Odin changed Loki's look entirely to look more like an Asgardian rather than a Frost Giant by touching him. Although Loki still can return back to his Frost Giant look, if he gets the freezing touch from other Frost Giants.
Full answer by surajit das: https://movies.stackexchange.com/a/119462 (CC BY-SA 4.0).
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