Those have been stored in fridge after purchase. I get no room to put in a large pot inside fridge even in our 2nd one.
I also buried another pot with Sichuan pepper. Fig & grape cuttings are buried at another place.
I think this way, I create something like a winter storage cellar. I cover the cuttings with plastic, but not for the chestnuts. So we create a storage place at about 30-40F. Cold, but not super freezing.
Maybe this is something I can build a rather permanent structure like this. Using some discarded bricks. And cover the “cellar” with wood and mulch.