Unlike oregano, marjoram is not hardy. It cannot be overwintered outdoors. If you keep it in a pot on the warm window sill, you can, with a bit of luck, see it through the winter.

Marjoram is not hardy
At sub-zero temperatures, the cultivated marjoram, which is most often planted in gardens, dies. You can try planting it in a pot and wintering indoors. However, this rarely works.
Oregano can be overwintered
In contrast to marjoram, oregano also withstands low temperatures quite well and is therefore usually cultivated in the garden as a biennial plant.
Before winter, you should cut it back and cover it with fleece, foliage or other materials to be on the safe side.
tips and tricks
The warmth-loving marjoram is native to southern regions. There it is always grown perennial. In our latitudes, it is too cold to spend the winter outdoors. It is therefore only cultivated as an annual plant.