I think that it is fine if legislators without scientific backgrounds have a say in global warming policies. They pretty much already do have a say in global warming policies. I think that it is okay for legislators to have a say in global warming policies, even if they don't have a scientific background because they can still be informed about global warming and make the right decisions.
Legislators are merely representatives; they can't have degrees in each field they have to issue votes about. However, they should definitely consult the latest scientific journals, scientific research, scientists, and also the people they represent in order to make sure they are both well informed and also being a faithful representative for their district.
Democracy doesn't say that you have to have a background in something in order to legislate against or for it. However, legislators really need to listen to the scientific community, and not big business or the religious right, in order to create and implement policy that concerns global warning of the world.
Climate change policies are no different than any other. Every politician is not an expert in every topic. They merely represent the people's interest(in theory.) Legislators can also draw upon experts in topics they aren't totally familiar with, so I don't see a reason why they shouldn't be included in climate change discussions, just because they don't have a scientific background. Did Senator McCarthy have a background in Communism?
In Congress, legislation is written and altered at the committee level. Those lawmakers who sit on scientific committees should have a science background whenever possible. Plus, scientists should also consult with these lawmakers to craft relevant global warming legislation. Those in Congress without the scientific know-how to handle this issue should stay out of the law-writing process until the issue comes up for a vote on the full House or Senate floor.