First of all, one move you have to master to see 2 of the secrets is to jump out and up one tile (see figure) with only the run and climb powers to aid you. It may be the hardest move in KS.
Secondly, the umbrella is a hidden power which is necessary for reaching several secrets.
There are 5 hidden characters.
2 in the Icicle Caves challenge route
1 in the Icicle Caves scenic route
1 in lab 1 (not really hidden)
1 outside, near Mrs. Soup's cabin
There are 4 additional hidden location.
The location of the umbrella which becomes accessible at the same time lab 1 does.
1 in lab 3
1 accessed through the Tundra Caves
1 in the Halls of Ice
There is 1 secret cutscene found with with 1 of the hidden characters.
Bulbapuck originally wanted every participant to make one image that could be used in a cutscene. The idea was shot down, but not before he'd made his picture. I wanted to use it somehow in the level, so this cutscene was born. The character driving the scene is of a knowledgeable species who appear in almost every level I've designed for.
While we're on the subject, the music heard in many of the hidden areas was cut from a demo Wako-kun gave us for a track he was inspired to make for the level. He was never heard from again, so I cropped the demo into something usable.
There are also quite a few missables. For starters, choosing one path over another when there's a choice between challenge or scenic routes often prevents you from seeing everything the other path has to offer. Mrs. Soup will change what she says as you progress through the game. There are 4 statements in all. The man in the lobby of lab 4 will also say various things as you make progress related to that lab. The tree house found near the Tundra Caves can be entered. Make sure you see it because I put a lot of work into that one screen.
After finishing the future section, the "scene" at the top of the elevator plays out a little better if you head right not left.