Yes, but the easiest approach is to photograph a stationary snowflake, not one falling through the air. The linked examples are likely single flakes positioned so they’re sharply lit, with the camera focused very close. A macro lens on a DSLR is ideal, but many phone cameras can also do decent close-up snowflake shots if the flake is still and you can focus close enough.

Photographing falling snow in crisp detail is much harder. You need a very fast shutter speed—roughly high hundredths to thousandths of a second—so the flake doesn’t blur from its movement or the wind. For a true close-up, the flake also has to pass very near the lens and land within the narrow focus zone at the exact moment of exposure, which is difficult. In heavy snowfall you might get lucky, but it’s not the practical way to make detailed snowflake images.

So for best results: find an intact flake that has landed, get as close as your camera can focus, and use strong, careful lighting. Falling snow can be frozen with a fast shutter, but detailed macro-style shots of airborne flakes are rarely easy.