Generally, not until and not before have the same meanings. There tend to be slight differences in the way we use them in sentences, but these are more about how they sound to us as opposed to what the sentences mean. If I were to write your four sentences, this is what I would say (even though I could write each sentence in the same format and they would be perfectly fine): 1. A. Until coming to Beijing, I hadn't seen snow. B. I hadn't seen snow before coming to Beijing. 2. A. Until the deadline comes, I can hardly complete the task. B. I can hardly complete the task before the deadline comes. I honestly do not know from a grammatical point of view why these sound better to me. I suspect it has something to do with the word "until" feeling like a limitation of some kind whereas "before" is a neutral representation of time on the continuum of "before, during and after".

until with one l : )

I can hardly complete the task before the deadline arrives is a little awkward. and the second sentence should read "deadline arrived" to be grammatically correct but it seems you want to use arrives.

1. A. I havn't seen snow untill I came to Beijing. B. I havn't seen snow before I came to Beijing. 2. A. I can hardly complete the task untill the deadline comes. B. I can hardly complete the task before the deadline comes. I had not seen snow until I came to Beijing. Before I came to Beijing, I had not seen snow. I can hardly complete the task before the deadline arrives. I hardly had time to complete the task before the deadline arrives.

@freewords: Thanks for sharing your oppinions. :D