So I have to suspect you are mixing up a couple of different but related stories?
Iceman, the 1984 film, covers much of the plot you describe. A neanderthal man is found in a block of ice and thaws out because he had eaten flowers that acted as an anti-freeze. He is kept in a huge room in the lab that is made up with neanderthal era flora (and fauna IIRC).
He quickly realizes he is in a sort of prison and begins to find ways out. One day he see's the lab's helicopter fly over the glass roof and believes it is a spirit guide coming to take him away. He eventually escapes, injuring (killing?) one of the lab workers on the way. They take off in the helicopter to find him, and dies when he falls from the helicopter after they approach to pick him up.
The end is him falling through the air, spinning, seen from above and shot against the ice and snow below. Not exactly an ice tunnel, but not entirely impossible to confuse it with one.
And then there's the 6 Million Dollar Man episode, in which Bigfoot lures Austin down what could easily be seen as a tunnel of ice. And back out again. They re-used this (probably expensive) set on many other shows, and it's not entirely impossible a show or movie as you describe.
Others have mentioned The Ugly Little Boy, which I didn't know had been filmed (I read the story as a kid). After watching it on YouTube and scrubbing back and forth, the only thing like that is a sort of metallic cylinder that comes down from above. But there's nothing like someone being inside it, and you only see it for seconds, and the people, a boy and woman, just sort of fade out - super cheesy. It is not at all like your description. I immediately recognized the time machine as one of the small theatres on the second level of the Ontario Science Center. The production values are making my head burn.