Given Loki is an orphan from Jotunheim not a child of Asgard why would he look like his adopted family?
The Frost Giants are not portrayed as looking human, does the fact that he was adopted change his appearance in some way or is it part of Frigga/Loki's "tricks"?
If I am not mistaken Odin changes Loki's appearance by touching him in Thor in a flashback scene. So Odin intentionally changed his look and then adopts him. His real look appears when he's attacked by a Frost Giant's freezing touch.
There is no explanation of Loki's small size as compared to Frost Giants but in comics Laufey kept him hidden from his people, ashamed of his son's small size.
There are further answers present on SciFi.SE.
During the flashback, when Odin picks up baby Loki, Loki's blue skin turns to Asgardian skin. When he is grabbed by the frost giants, his skin reverted back to the original form, not only changing the color, but the texture as well (if you noticed, the frost giants have ice like skin, presumably from being in Jotunheim so long). Loki's size is actually talked about in the original Norse myths.
Frost giants are different from humans in many ways, one of them being that the males carry the children and give birth. Loki had two older brothers (their names escape me at this moment), both of whom Laufey (Loki's father) birthed. They are much older than Loki. There was much pain in Laufey's labor of the two eldest because they were so big. Laufey was the king of the frost giants, and so naturally he was huge, even for a frost giant. When Laufey was giving birth to Loki he had no pain which concerned him. It turned out, Loki was a runt and so the maid asked if he wanted to get rid of Loki. Though sometimes cruel, Laufey was not heartless, and kept the little frost giant.
Not long after Odin came and the war began, killing both of Loki's older brothers, who Loki never got to know. Laufey had to leave his now only child and join in the battle against the Norse god. the rest of the story is shown in the movie. Odin takes the small frost giant and raises him as his own alongside his biological son Thor who is older than Loki. They do not know they are not related until many years later as adults. That wouldn't have mattered to them anyway. They were brothers by bond, not blood, which in a way can be much better.
So there you go, sorry it was long, but I love mythology. I hope I explained it well enough and answered the question. :)
