The ticket booth operator lists a bunch of locations that would be counterintuitive to travel to (Saskatchewan is in central Canada, Hudson Bay eastern Canada, Nome is in FAR western Alaska, a whole trip across the continent westward, the Klondike is in the Yukon, a southwest backtrack) until you realize he was humoring the kids and trying to say that there's no way to travel by train to the north pole, which is a bunch of ice floating in the Arctic ocean which public transport doesn't go within 1000 miles of. There isn't even a land bridge between Canada's Ellesmere Island and Greenland. Had the kids had the $3000 for the ticket, he would have had to admit he was making stuff up or make up a story about train service not being in for one of the lengths of the journey.
This also explains why one of the "stops" he lists is the Aurora Borealis, which isn’t even on Earth.
Why do Frosty, Crystal, and all other snowpeople say "Happy birthday!" when they come to life? They're saying it to themselves, because they've just been "born."
Hinkle is after the hat because he discovered its magic. But if you think about it, his plan to use the hat would never have worked, even if he had gotten it back. The whole reason he threw it away to begin with is that he couldn’t get it to work; had he recovered it, odds are, the magic would have continued to refuse to work for him.
At the end when Santa dropped Karen off at her house, he left her on the snowy roof where she could easily slip and fall to her death.
Karen's parents must have been very worried about her when she didn't come home from school. Even if one of the other kids told them where she went, learning that she hopped onto a train headed toward the North Pole would probably have been no consolation. She naïvely thinks she can take Frosty to the Pole and be home in time for supper, but it's probably much later than that when she finally does get home, and who knows how long it would have taken her to get home if Santa hadn't given her a lift?
