The problem is that areas had record cold this past winter, and "deniers" get slammed for correlating a weather event to global climate change
Record cold can be evidence for global warming. The key is to understand what "warming" actually is: adding energy to the system. Consider a glass of water. What happens when you add energy to it by shaking it? The answer is, it sloshes around -- the maximum height of the water surface gets higher, and the minimum height gets lower. Or consider the refrigeration thermodynamic cycle: one part of the system gets colder even though the total energy of the system is increasing.
That's not to say that record cold is always evidence of global warming, or indeed that it could never be evidence of an oncoming ice age. I'm just pointing out that the issue is more complicated than "record cold = cooling" or "record heat = heating" considered in isolation. We only know that record heat actually is evidence for heating because it's been observed as part of a larger pattern and was predicted by climate models and such (i.e., all the actual science that climatologists do that a Fox News sound bite is inadequate to explain).