I think other states have spiders and snakes, too. Just so you know...
As far as the weather, we do occasionally get a hurricane come inland - Charlotte was devasted several years ago. But usually the risk is much reduced unless, of course, you live on the coast. NC can and does get major hurricanes, just like every other Atlantic coast state.
We have been having some tornadoes this spring, but they are pretty rare, really. Usually an F1 or F2 at the most. The last tornado to hit my city was in 1936, although the interstate nearby was hit last week. But again, tornadoes are really pretty rare - maybe a few days in the spring when we have warnings.
Now ice storms are a different story!! We get them all the time - and they can be a pain because it takes several days for the crews to clear and rebuild the power lines. Snowstorms are typical in winter, especially in the mountians, of course. We have had much less snow in the Piedmont for the last several years - but we can and do get 10 - 12 inches occasionally.
If you live in NC and hear a forecast of snow, better hightail it to the grocery store and get bread and milk - we stock up even if the forecast says "scattered flurries" and only a few flakes fall. And we drive like morons in it because we don't really know how to do it.
But overall, we have beautiful 4 season weather and lovely geography.