It's common to use a cold frame in a raised bed. It doesn't turn it into a greenhouse, but it extends seasons, so it could keep winter growth alive and lets you start earlier in the spring.
Search Google
https://www.google.com/search?... and look at images. More examples than I cold describe. What almost all have in common is hinged tops, removable in warm climates.
You could probably make a cross-braces light frame and cover it with clear vinyl. Or buy some double wall greenhouse panels and lay them across the border.
