Maybe just me or where I am from but I can't imagine leaving out 'the' in this sentence. By having 'the' in the sentence you are stating that the weather in August (good or bad) is not to your liking. By leaving it out it sounds like you wanting August to be totally devoid of all weather types.
I agree with Glyn. You really need the "the" in this sentence, and Marek's alternative. The only time it could be said without "the" is when you mean weather to be synonymous with storms. Pilots use it that way, the word weather as a shorthand for bad weather for flying.