Ah, one of those "deep" topics. While I have no theory of my own about Mr. Thicknose, I do agree with Malte279's theory of him no longer wishing to live, and listed my reasoning for doing so. I likely made several errors in my understanding of him, but I tried my best.
For one thing, by him telling Littlefoot to ask nothing else, I believe he meant that literally, not the everyday usage generally meaning "don't bother me right now." He seems to be the type of character who means word for word whatever he says. That attribute doesn't automatically make someone honest, I just meant that he doesn't really seem to be a big fan of metaphors, puns, and figures of speech. No messages to be assumed, just to be taken at face value.
My point being is that, since he seemed to spend his life teaching others, saying "no more questions" seems to indicate he has given up on teaching, since teaching and being asked questions go hand in hand. So since his life seemed to revolve around that job, without it, it may just be that he no longer wished to live, for without a purpose, there tends to be a lack of will.
Secondly however, would be his standing in the cold long enoug to have been covered by snow. His common knowledge certainly seems abundant, if not only for the fact he has lived so long and has experience. I know that the snow in the valley was the first to have been seen by the returning characters, but if the eight movie isn't so far after the first time-wise, perhaps it had snowed there several times but the main characters are seeing it there for the first time.
My point being there is that, as is common knowledge that in cold weather you must keep your body moving to stay warm if without proper covering, perhaps he just stood there so his body would eventually freeze. It was certainly not that he enjoyed standing there, as his tone of voice with his question response displayed much discomfort on his part. If someone is uncomfortable, he or she tends to resolve that, so by remaining uncomfortable for so long (the length is revealed by the amount of snow on him) it would seem his comfort no longer mattered, indicating perhaps that his life no longer mattered to him, thus he remained suffering, hoping (or at least knowing) that his end would certainly come.
When he saw Littlefoot, Cera, and Petrie leaving the valley and learned what they were intending, you could tell his outlook on life brightened, since his countenance brightened and his voiced displayed some pleasantry as he said, "I'm going with you."
If Malte279's theory is correct, then you might say, as Littlefoot was the one who insisted that they go into the Mysterious Beyond after Ducky and Spike, that he saved Mr. Thicknose's life. If he hadn't decided to leave, Mr. Thicknose would have most likely stayed under the snow until he was no more, since he apparently had no intention of moving before he saw them.
Also, in response to Saft saying how he agreed to go with them because their parents wouldn't forgive him if they all knew he just let them go, perhaps he did just want to see the wonders of beyond the Great Valley, and so maybe saying that to the kids was just a decoy reason for leaving, since he was already in bad standing with some others there, and he may have simply not wanted to say that he just wanted to see the outside, because that would give away his secret which had not yet been revealed. Again, just an agreement, not a whole new theory. Later!
