I've successfully used both cold stratification and outdoor planting of Yellow Buckeye, a relative of Horsechestnut (yes, you appear to have a horsechestnut, given the spiny husk on the nut). The outdoor method is easier but comes with an external problem: squirrels. They love to eat the nuts, and dug out and ate probably half of the buckeyes that I planted. Since I was just planting the nuts in weedy/woody margins of a local park, this was no big deal to me, but if you're looking for a permanent planting at your own place, it could be a major problem.
When I planted a nut on my own property in the spot I wanted a tree, I protected it from squirrel/vole/other rodent predation as if it were a seedling. I planted the nut about four inches deep, covered it and the surrounding area with a couple of inches of wood chips, then used a stake to tie a cylinder of hardware cloth over the entire planting area. (Hardware cloth is 3/8" steel mesh). I sank the cylinder into the wood chips to keep voles from tunneling, then used ground staples to provide additional stability. I use this kind of cylinder to protect all of my smallish trees until they're too wide for voles to girdle or rabbits to use as teething tools.
If you're planning on "lining out" a row or block of seedlings, then you can adapt my method by stapling hardware cloth or chicken wire along the top of the ground. Note that voles can easily get through the holes in chicken wire, although I don't think they'd dig up the nuts.
One of the most important factors in planting any Aesculus (Horsechestnut and Buckeye genus) seeds is timing - the fresher the seed, the better the germination. So, if you're going to try the outdoor method, do it now.
If you want to try cold stratification, plant the nuts in containers and store in a refrigerator (thus controlling the temperature and timing of germination). You don't plant them until spring, but you will need some kind of light source for them if they sprout in the containers over the winter. Generally, though, you control germination yourself by removing the containers from the refrigerator a month or six weeks before you intend on planting them out. If rabbits are an issue, you will have to protect them from being eaten for the entire summer. The cylinders I described above are an excellent solution to that problem - because they leave the tree open to the elements, they can be left on the tree for years with no issues with fungi, insects, or rot.
UPDATE
Here is an example of the cylinder I wrote about above; it's around a one-year-old yellow buckeye:
Note that if you spray-paint the mesh black it disappears into the landscape.
