"Must" implies authority on the part of the speaker. So, as a teacher I can say "You must do your homework" but not "You must bring your passport to the airport." Only the security guard or ticket agent can say that, I would say "you have to bring your passport," because it's a requirement but I have no authority.
These sentences don't really sound "right." I would make the following changes (everything always depends on the context, maybe I'm not seeing it):
Hunger will / has to follow after the long drought. (logically)
You should win，if you do your best． (nothing is certain, but you are very good so I really believe that you will win if...)
It will snow tomorrow. (I can't think of anyone who can oblige the weather to do something. You might say, "I'm certain it will snow tomorrow" but not more than that.)
If we aren't careful enough, things will be worse. (can you explain the context where a 2nd conditional would be used? I'm sure it's possible but it's your problem not mine!)
If he abandons her, she will go mad．(if you use the 1st conditional here, you are insisting that the madness will be a result of his leaving her.)
It's possible that you are confusing the uses of "must" in deductive statements and statements of obligation (it is really confusing, after all). You have to remember that the same structure can mean two different things depending on the context. For example, "It's 9:00, she must be at work." This is something my wife's boss might say to describe the obligations of her job. But it's possible that I would say the exact same sentence if, in the morning, someone asked me where my wife was. In that case, I don't oblige her to be at work, but I can assume (based on past behaviour) that at 9AM, she's at work.
