Since Stack Overflow uses Markdown for parsing, you can simply write in Markdown and then format your e-mails with a Markdown-to-HTML parser.
One of these is Markdown Here, which with the click of a button turns your Markdown-formatted source into shiny rich text, even with syntax highlighting.
It's available as a Chrome extension, and Firefox / Thunderbird add-on, which you would use. The developer is very supportive when it comes to bug fixes and feature request, and I've seen him here on Stack Exchange as well.
To write the actual Markdown, I'm not aware of any Thunderbird add-ons that'd get you the Stack Exchange keybindings, but you can use an editor like the online-markdown-editor I forked from the official Stack Exchange tool and hosted on GitHub. It supports the same keybindings.