This question is getting close votes as 'primarily opinion based'.
Shouldn't it stay open with an answer "There is no data"?
The question is pretty straightforward: For what proportion of the earth's history has there been permanent ice?
The OP does not ask for an opinion, neither are there answers that are opinions, debates, vague claims etc.
What may be confusing here is that the OP is quoting an unsubstantiated claim from Wikipedia, but that's exactly why he asks the question here.
If we do not currently have an answer to a good question, then the question should remain open and unanswered.
If a question is fundamentally unanswerable, then it is out of the realm of science and therefore out of scope on this site. I have not seen any of such questions on Earth Science, though.
I don't think the question is primarily opinion-based, even if perhaps it's not possible for me to have a satisfactory answer given the current state of our science.
I might be happy to accept as an answer a response that clearly outlining reasons why we cannot hope to answer this question given the current state of our science. Then, if science advances sufficiently within my lifetime I could revisit the question and accept some other answer.
I might also accept an answer that demonstrated that in principle we can never aspire to answer this question. Again, if the person turns out to be wrong then I can always remove the tick from the answer later on.
This is a perfectly clear, reasonable, and on-topic question, and as such it should not be closed.
I believe that it should remain open, and that it would benefit from an expert in the field answering with a summary of the current state of knowledge on the topic, and an explanation as to why it cannot currently be fully answered (if that is indeed the case)
