https://sheffields.com/seeds-for-sale/Juglans/nigra/////Northern//762/Black-Walnut,-Eastern-Black-Walnut/Black-Walnut,-Eastern-Black-Walnut
I’d give them the soak and then put them in a ziplock bag with some moist (not wet) peat moss and just store them in the back of your fridge. Every once in awhile check them for signs of mold. At some point in the spring they may start germinating in the fridge or you can pull them when the chance of frost is gone and store the bag somewhere safe outside away from critters. Or you can pot them up or directly seed them even if they haven’t started germinating yet and they’ll do their thing eventually. You can directly seed some now too if you protect them from rodents above and below ground. Then they can cold stratify naturally all winter and then start rooting first thing in the spring when nature tells them they’re ready. These nut trees put out strong, deep taproots so direct seeding is really the way to go for the healthiest tree. They’ll be more drought resistant too and you don’t have to worry about transplant shock.