Humm Birdie

You most certainly can! For chestnuts, the video that explained it to me best is one using a bucket method:  
I'm not entirely sure if this method works for walnuts and hazelnuts, but I think it's worth a try since it doesn't take much.

you can also just spread the seeds on a prepared seedbed in autumn, and cover them up with a bit of soil/mulch, then cover them up with a dense steel mesh, so it's protected from mice, squirells, and the rest.

Also, plant many of them, don't put all your faith in just a seedling or two. And by next autumn you get some free trees, what's better than that?

Hey, thanks. I've been a long time lurker here and just felt I can share something here

I also have some firsthand experience with this - We've grazed our pastures just with cows for around 6 years now, it's a bit different than in your area, because the land here was already fertile and overgrowth was a problem in some areas. So there were some grassy areas that were already slowly becoming forests with a lot of blackberries and vines blocking the passage. The cows helped a lot with clearing both. Once a bull got a bit stuck with horns into some vines, and he just started wildly turning his head left and right and pulling back really hard, which in turn pulled a large number of vines from trees. And his reward, after he finally got unstuck, was a large number of fresh vine leaves and shoots. And some vines remained around his horns still, even after he was free, so he looked really majestic, like he had a crown

If you clear the area with animals, I think it's the fastest, but also takes the most time and worry that they might escape. But they are a massive help.

Cows don't like blackberries though, they are mostly good just for trampling them sometimes, and eating resprouts that occur after you do some clearing in the autumn with shears and chainsaw. So with cows + goats I think it would go even faster.

I would clean/mow around the trees I would like to leave, put down a cardboard ring and whatever mulch I had available, preferrably lots of leaves or woodchips, along with some compost or manure.

Then, depending on how much time you have, and what you want to do there, you can clean more areas, pile mulch there to start improving the soil and plant trees.
However, since I myself don't have much time, and some nicer areas I still need to plant perennials into, I would just leave most of the overgrowing patches, try throwing some desired tree seeds in there, and wouldn't do much there for a couple of years, until trees would start to be visible and around an inch thick. Then I would also start minimally tending to those areas, so I would watch out to keep the desired trees and try to keep them a bit mulched with at least the surrounding sun-stealing vegetation, which I would chop ~once a year and put it around as mulch.

Grazing with animals such as cows and goats would be also a good option to help with clearing brush and grass, and improving the soil of the area, but make sure you well protect the trees that you want to keep.

If you have even more time and resources, you can also scatter clay balls and seed the entire area with soil improving cover crops.