Green woodworking: wood starts molding. A problem?

Hi woodworkers,
I recently got a bunch of wood from a European nettle tree (Celtis australis). It’s wonderful to work with. The locals use(d) it for all types of tool handles.
I put the round wood in a barrel to keep it from drying too quickly and it’s (as was to be expected) starting to mold. Do you see a problem with that? How do you keep your green wood green without getting mold?

It's not a problem until it is! I've stored green wood temporarily (1-2 weeks) in plastic. It might get some permanent staining from the surface mould, but it's typically just a surface cosmetic issue and not a structural issue. If you wait too long, the fungi will damage the wood -- you might get some aesthetic spalting, but are likely to also have the result be significantly softer and weaker than your original wood (not great for tool handles).

If I want to keep something green and in good condition for months, I cut it to size and put it in the freezer. You can store it for some time in this state, and then thaw it and work it green. Of course, there's limited space in the freezer, so one has to be pretty selective when deciding to do this!

Thank you for the answer. I’ll select a few pieces then and try your freeze trick. The rest I guess I’ll have to work after drying then