I think green looks great with burgundy and it doesn't necessarily have to look like Christmas. There are a few on this link that don't look that way to me. Also, golds, blues, beiges/tans also look great with burgundy. You could always introduce a another color or two that would help keep it from looking Christmasy. There are some that have several colors that look great.
https://www.google.com/search?hl=en&...lt%22&tbm=isch