(Question)
Is it safe to paint a cold frame for growing vegetables? Or is it better to just paint the outside of the wood to make it last longer? thanks
(Answer)
Since you are wanting to grow vegetables I would not recommend painting your cold frame as I was unable to find a scientifically verified non-toxic paint.
There appear to be very few choices for verified safe treatment of wood for raised beds/cold frames.
One non-toxic option for wood preservation is pure RAW linseed oil (not boiled, which can be toxic). Carefully read the label. Please note that linseed oil can be slow drying and can be flammable. It can also be a food source for mildew. That said, it is water resistant and can help protect wood from the elements.
Good luck with your cold frame