We got a bit of snow this past weekend, and while out and about I caught a snippet of conversation referencing the snow and mentioning global warming. I will say that discussion did not exactly involve the perhaps expected questioning that constantly pops up of how there can be heavy/early/late/whatever snow if there is supposed to be global warming. What the people exactly were saying is not really important, but as someone who is relatively knowledgeable about weather and climate what was striking was how unknowledgeable these ordinary people that I overheard were.
I am obligated to give my standard note about ignorance. There is nothing wrong with ignorance of a subject per se. Problems come from certain sorts of responses - disregard of what is known about and those who are expert on the subject, filling the knowledge gap with demonstrably false information and ignoring correction, etc.
It is easy to get a little isolated at times and forget the minimal knowledge of most people when it comes to climate science. Thus it is important to remember to highlight "the big picture", as at Skeptical Science - because of human activities the Earth is warming and will continue to warm with net negative results.
Not sure how best to do so, but I think ground can be gained with many of the people who have a major dearth of knowledge related to weather and climate. There is probably not some single way. Some may respond to the simple authoritative statements like in the paragraph above, some may respond to certain details such as the basic physics, etc.
That malleable group though may be rather small at very least in the US because of the politicization of the issue of climate change here. The Republican party has virtually made denial of climate science a litmus test, and partisans tend to follow the stances of their leaders. Yet the higher the education level among Republicans the greater the tendency to deny the science. There are interesting ideas to explain this like that "more educated" Republicans are more detached from the science and more politically polarized and that they are more likely to come into contrarian garbage that can be believed to disprove climate change. On the flip side of the coin at least there are many on left who do accept the science even though they are clueless about it. The correct thing for the correct reason is best, but the correct thing is an acceptable runner-up.