Yes, it is fairly natural. Your meaning is that a booking may only be made for dates between now and March of 2016--a calendar year forward. The word, "through" represents 'between now and'.
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AnonymousYou can only book through March 2016.That would not be natural in British English. I'd say 'until'.
fivejedjon AnonymousYou can only book through March 2016.That would not be natural in British English. I'd say 'until'.You're right. It's an example of the US/UK differences in English. The word through is used in the USA, while the word until is used in the UK.