I have a simple question, in the spirit of "What evidence would it take to prove your beliefs wrong?": How many years of dropping temperatures does it take before global warming is no longer an acceptable hypothesis?
Well, never. It's always an acceptable hypothesis, because maybe you haven't considered all the evidence yet. What if CO2 causes global warming exactly as scientists predict, but the Sun is going out?
However, if your question is, would several years of falling temperatures make it more likely that global warming due to CO2 doesn't exist, then here is the answer:
It depends. There are several other major factors in play determining the temperature of the planet beyond CO2. For example, if average sunlight received dropped for 10 years in a row, a rise in CO2 might not be sufficient to counteract that. However, if you didn't find anything else in play, it would be strong evidence that CO2 does not cause warming, at least not on the time scale you're looking at.
This would be an very surprising result though, since we know that CO2 is a "greenhouse gas" - it traps heat. If higher concentrations of CO2 in the atmosphere did not cause increases in temperature, it would be weird and shocking.
Models that predicted a monotonic rise in temperature due to mankind's influence can not be used to extract mankind's putative signal when it turns out that they were wrong.
It's important not to let global warming hysteria color your view of the science. There's a radical difference between "mankind is the dominant force of global climate change and mankind is causing catastrophic global warming that we must avoid at all costs" and "mankind is adding a small delta below the noise level of natural climate", and the range of things in between. If it does turn out that the sun is getting dimmer and that turns out to have a major effect on climate (and I have seen climate scientists flat-out deny this is true), then it bounds the effect man can be having and moves us closer to the second statement.
Every year that is colder instead of warmer bounds the warming effect we can be having. Frankly it's already pretty small.
That's not true. You could have an arbitrary number of years that were colder in a row, with rising CO2 levels, and still have a world where CO2 causes a temperature rise. It would simply require a countervailing force that's stronger.
The noise level is irrelevant; I'm not sure why you would bring it up. If there are naturally forces that fluctuate up and down in a random walk, and CO2 is a much smaller but consistently up force, inevitably we'll wind up with increasing temperatures over time. You could argue there are larger climatic signals (not noise) that we should be concerned about, but what you actually said is simply wrong.
Trying to transition global warming fearmongering into "climate change" fearmongering should be laughed out of politics. Climate science has a long way to go before it proves that "climate changes" are both significantly caused by man, are significantly worse than what would have changed anyhow, can be significantly improved by any particular action we can take, and that such actions would be cost-effective. (When you start to look at the problem like this and see what is really scientifically necessary, you start to realize just how far we are from this, by even the most optimistic estimates.)
(The word "fearmongering" in my previous paragraph is not an accident. It's great to research climate change in the spirit of science and look at what's really there; science isn't fearmongering, fearmongering isn't science. There's a lot of very non-scientific stuff occuring in the global warming hysteria field, though. If you want to tell yourself that it's only the non-scientists doing that, I won't argue the point, but it doesn't make the hysteria go away.)
