Statements about the Future
There are two ways of denying that the future is real. One is to accept statements about the future as true but to interpret them in a way that does not require the existence of their subject matter. This is a kind of fictionalism or ersatzism about the future. (It's interesting by the way that abstract ersatz futures clearly don't count as futures, whereas it is controversial whether abstract ersatz worlds should count as real possible worlds.) The other way of denying the reality of the future is to reject the assumption that statements about the future are true. Then no fictionalist or ersatzist story needs to be told to account for their truth.
On this view it's not true that I will sleep tonight. Nor is it true that I won't sleep tonight, at least if this is understood as Tonight(I do not sleep). It is presumably true if understood as Not(Tonight(I sleep)), though this depends on what truth value statements about the future are assigned and how 'Not' behaves with respect to this truth value. If it's not true that I will sleep tonight then it is either false or neither true nor false. In the latter case we have to decide what 'Not' does when it is applied to the third truth value. Personally, I find it somewhat more natural to say that if the future doesn't exist then statements about the future are false, not neither true nor false. Compare the spatial analogy: Since there is no place north of the north pole, it's not true that some people live north of the north pole. Is it then false or neither true nor false? I'd say it's simply false.
Some who deny the existence of the future argue that even though statements about what will happen later aren't true, they will become true later. At least if they are statements about sea battles: even though it isn't true now that there will be a sea battle tomorrow, nor that there won't be a sea battle, one of these predictions will become true tomorrow, and probably stay true thereafter. On this view, a token S of a sentence, uttered at time t1, has its truth value only relative to another time t2: relative to now the prediction is false (or neither true nor false), but relative to tomorrow it may be true. This is a kind of temporal double-indexing, or rather triple-indexing as we probably need two temporal indices even before worrying about the future. But the real problem is that the current proposal doesn't work in general. For "it will be true tomorrow that there is a sea battle" is a statement about the future just as "there will be a sea battle tomorrow". It even seems to me that the two are equivalent. So nothing is gained by rejecting the latter but accepting the former. If one claims that statements about the future aren't true one can't consistently say that some of them nevertheless will become true in the future.
A slightly different version of your north-pole analogy might come out slightly different, though. I'm inclined to think that 'no-one lives in the place north of the north pole' is neither true nor false, because of presupposition failure. It also seems to me to be a better analogy to the temporal case, although I don't really have any argument for this position, and syntactical similarities (at the very least) argue in favour of your analogy.
Also, I don't think it's quite right that "one can't consistently say that some of them nevertheless will become true in the future." You can say it; what you can't say is that it is true. I'm not sure that helps anyone, but perhaps providing a theory about how assertions about future events work would allow someone to distinguish between "it will be true tomorrow that there is a sea battle" and "there will be a sea battle tomorrow"?