Story about a boy from a cold world, who comes to Earth through a portal

I suspect this is only a partial match, but the novelization of Through the Dragon's Eye probably follows the same plotline as the TV series, which has Charn as a character in a cold world, followed by one of the protagonists.

Fortunately, the inability to read also afflicts Charn, allowing Jenny to display a written message to her friends when Charn forbids her to divulge his presence (She tricked Charn into allowing her to knit a scarf due to the cold of Pelamar, drawing out a pattern that actually spelled out "HELP! CHARN!" without him knowing, which she could then show to the others over a video phone). Although Gorwen is able to defeat Charn, he is dangerously weakened, nearly killing himself before the last Veeton is discovered and the Veetacore restored. Although the show ends with the children returning to their school at apparently the moment they left, the presence of their notebooks and three miniature versions of the Veetons they recovered proves that the experience was genuine.