There are blizzards in California. Maybe not where you are, but they do occur. Tornadoes have occurred in every single state, as well. It’s a matter of frequency and severity. Our tornadoes are very seldom as large or as lengthy as midwestern ones. A true blizzard is practically an unheard-of thing here. Earthquakes, we’re at moderate risk due to proximity to Charleston, but I’ve experienced nothing stronger than a tremor in my lifetime.
To me, it would be nerve-wracking to live in a place where there was a severe risk of any of these. It’s possible to get any of them here but it’s not a severe risk. Worst thing that has ever happened to me was sleeping through the roof being blown off my house by Hurricane Hugo. Sounds like that sort of thing would wake you up, but the wind howling kind of masked it, I guess.