My seedlings do much better doing the soak, damp fridge and start indoors vs planting directly outside. I did both last year, and my seedlings are much further along than the direct sown ones.
I store all my seeds in the fridge to keep them stable. For cold stratification, after soaking overnight in warm water, I put them in a small ziplock bag (can find in the craft sections of stores) and a damp paper towel (I use those face cleaning pads, cut into quarters) for three weeks. Then I pull them out and use whatever method is my current favorite to germinate them. (on the rocks, direct planting outside, planting into a seed starting pot. etc
I do check them periodically - I have had some crosses occasionally start germinating in the fridge ~Jan