Since we see in a flashback that Baby-Loki is picked up by Odin, and begins to switch to a human appearance immediately, that some aspect of Odin’s magic, or “Asgardian Magic” more generally, causes Loki to appear Asgardian.
Conversely, it could be that Jotunheim itself, and the Frost Giant magic, bestows the blue skintone to its inhabitants.
A few corroborating points to this theory:
- While fighting on Jotunheim, Volstagg is injured, and his wound turns bluish in color;
- When Loki is attacked, his skin turns blue while his attacker is holding him, and then reverts once he is let go.
- When Loki lifts up the magical blue cube which contains the Frost Giant magic, he slowly begins to turn blue, only reverting to Asgardian appearance when he releases it.
My personal theory is that, if relieved of his Asgardian clothes and weaponry, and left on the Jotunheim “planetoid”, Loki would indeed slowly revert back to his naturally blue “Frost Giant” appearance, though whether or not he might begin to grow in stature to become a full-on Frost Giant is still doubtful.