Next year, the students will have to do something different.

Is it possible to omit the 'will' above without changing the meaning?

Yes and no.
1. Yes, you can omit will and still have the idea of future.  As you know, a will form and the present tense form can both be used for a future time meaning.
2. No, the nuance is slightly different.  Here is (approximately) how:

Next year the students have to do something different, namely, sign up for classes at least two weeks before the start of classes, because we need time to e-mail them some information about the class before it starts.  That's a new requirement that we've never had before.

Next year the students will have to do something different.  What they did this year was just not adequate.  I don't know what they will have to do, and I realize that it is a really difficult situation to resolve, but when the time comes they will be faced with the decision of what to do, and it will have to be different from this year.

In summary, the will connotes a sort of 'not knowing now' which is not present to the same extent when the present tense is used.

But at this point we can revert again to the "yes" answer and say yes it would be possible to omit will without changing the meaning, because it would not be completely anomalous to interchange the opening of the two examples above, placing the will version in the first example, and vice versa.

It's a little like a Necker cube. 

CJ