Tree seedlings transplant timing?

I collect chestnuts, acorns, sycamore ‘helicopters’, beech nuts, rowan berries etc over the last few years during Autumn, and stick them in pots in compost over winter, usually in the garden shed. Often they won’t germinate, but they regularly do. I now have a couple dozen tree saplings / seedlings and think they should probably be potted on for further growth. They range from 3-4 inches to 2-3 feet tall. When’s best and any advice for best results?