grammaticality - Can "since" and "wouldn't" be used in the same sentence?

For example:

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.

Answer

There is absolutely nothing wrong with

Since it's raining, wouldn't it be a good idea to bring an umbrella?

Look at a few other constructions to see how natural it is:

Since you're going to the store anyway, wouldn't you like to pick us up some ice cream?

Since our success is uncertain, wouldn't we be well advised to consider how to minimize our risks in case of a downturn?

The first clause assumes a fact, and the second balances it with a speculative counterpoint. That is grammatical, unexceptionable and, incidentally, one way to make a sentence interesting.