I think it's safe, but that certainly varies by the location, season, and individual. I wouldn't worry particularly about the big cats; unless you're a relatively small person who acts like prey, the odds seem quite good to me, day or night.
If you want to worry about an animal, in some locales snakes will sometimes be out more at night, but ... so what?

I think the biggest risks to night hiking are falling, taking the wrong turn at a trail junction, missing an important water source, that sort of thing. And of messing with your sleep cycle. It can be a truly excellent way to cope with hot weather.