These differences in the distributions have a small impact in some situations and large impact in others. They have been measured many times. In fact, even the differences between the sexes' "climate IQ" have been studied by various papers.
One of the most recent ones is the 2010 paper
The effects of gender on climate change knowledge and concern in the American public (PDF, HTML, Google News)In an article in Population and Environment, Aaron McCright of Michigan State University found that women have a lower self-confidence and higher gullibility when it comes to the questions of "climate change". As a result, they're more likely to believe that there exists a "climate threat".
The differences are of order 10%. Various "chicken little" indices are 10% higher for women than for men; the percentages believing that the effects of global warming are already occurring in the world around us are 54% (men) - 59% (women). The beliefs that most of the changes are caused by humans show a larger difference: 56% (men) - 64% (women). These differences are kind of statistically significant although the confidence level is not too high.
The author of the study apparently believes this sex poodle pseudoscience as well (no surprise, otherwise he couldn't be employed by the environment program at MSU) so the terms he is using in the interpretation of the data are sometimes upside down. Nevertheless, the data speak a very clear language.
There have been several related papers discussing similar questions in the past.
Of course, when you attribute the observed differences, it doesn't have to fully boil down to the IQ differences. Women are simply more likely to be led - and women also may be more hard-wired to worry about the generations of their children etc.