Since it's raining, wouldn't it be a good idea to bring an umbrella?
That sounds OK, but I'm not sure if it is.
What about these alternatives?
Since it's raining, isn't it a good idea to bring an umbrella?
I thought that this might be grammatically correct because "is" is on both sides of the sentence. It doesn't sound right though. Why?
Since it's raining, won't it be a good idea to bring an umbrella?
For some reason this doesn't sound right either, but I don't know why. It sounds better than the second example, but not as good as the first example.