I harvest seeds in fall (Oct) when the wing on the samara is turning brown and the seed is still green. When the leaves on your tree start to change to their fall color or fall, the seeds are ok to harvest. It's not a big deal if you remove the seeds a bit too early, they will continue to mature at room temperature.
I usually sow in flats in Dec immediately after a 24 hr hot water treatment when the rest of my fall chores are behind me, and let Mother Nature take care of cold stratification. I fill flats 3/4 full of moist 5:1:1 mix (seed starting mix is fine) and spread the seeds evenly as I can on top of the soil, then cover the moist soil with 1/4" of screened sphagnum peat (or more seed starting mix) and leave them to over-winter in my garage with all my temperate trees in containers. Most germinate in March or early April. The 'in the fridge/ paper towel method' works fine for small batches of seeds..
I sow the seeds very densely, maybe as many as 100/sq ft. This ends up producing long, straight whips. I allow them to grow without pruning for a full year, selecting the trees I want and marking them with a piece of yarn tied to the tree. I look for trees with small leaves and short internodes or unusual bark characteristics. I might select 1 or 2 out of every 100 seedlings. Some of the whips get used in their second year for root grafts, so there is always a demand for J-maple whips.
These are just starting to poke their heads up, and maybe half of the seeds had germinated at the time I took the image. I started them for a friend but he was injured and I'm still holding them for him. They will be 2 years old now come March. If I remember, I'll add an image. They have all lost their leaves and are headed for deep dormancy as soon as we get some hard freezes.
Don't forget to plant some CLUMPS. I often plant 5-10 seeds in the same hole and thin later.
Al