It can't, but it can get digital hash, which looks a lot like snow (but is usually in color, mostly green)
I didn't either until I saw it for myself just recently. Usually, with no HDMI signal you would get a black screen, but I just had a bad HDMI cable and it actually caused snow on my screen! The bad cable still passed audio OK, and it would intermittently work if I wiggled it. I should also say that after about 30-60 seconds of snow, the screen did eventually go black, but when I wiggled it again, the screen would be all snow for about another minute. The snow looked just like an analog TV that was not tuned to any channel! I was surprised.