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You’re going to want fast shutter speeds (it’s a thing in video too) and since it tends to be fairly low contrast and often darker because of the cloud cover, most cameras are going to slow things down to get more light in.
So if you have control over settings on whatever you’re filming on, try higher ISO, faster shutter speeds and potentially a higher frame rate would help to but less sure on that one (I just do stills)
PhilDAS-
You’re going to want fast shutter speeds
I was going to go in the opposite direction. The eye has a shutter speed of the order of 1/10th of a second, and flakes fall at 1-2m.s-1, so they appear to the eye as streaks 10-20cm long rather than points as they would in a still image at a typical shutter speed for outdoors in daylight. I think I'd try stopping down to the smallest available aperture to get loads of DOF and a long exposure and see how that looks.
gbj_tester
Why does snow look more dense IRL then thru a lens or a photograph? It’s snowing right now, but every picture I take of it looks denser with the naked eye.