I mean, compared to CA, the winters can get cold. I think the coldest I ever experienced there (not counting wind chill) was maybe 0 degrees Fahrenheit give or take 5. Usually, average winter temperature stays in the 30's/20's, sometimes teens. Compared to other parts of the Midwest (Chicago comes to mind...), it's pretty mild. You might get a few blizzards in the winter, so prepare to dig out your car once or twice (my first time took 2 hours, with a tiny windshield scraper, quite a workout). The snow starts around the end of November, and lasts until March, maybe April if you count the occasional remnant snow fall. The summers can sometimes get humid, but nothing too crazy.
We did get a few tornado warnings, but because of the geography of Omaha, very rarely would a tornado actually touch down in the city proper; the closest thing I remember was when a buddy of mine sent me a home video of what he thought was a small tornado touching down on the outskirts of the city. The jury was and is still out on that one though. We did get plenty of thunderstorms in the summer though, those were actually fun to watch (from a safe location of course), spectacular light shows. And no, the Midwest in general does not get many (or any) hurricanes. Really gave away our native state with that last question