Sounds like you're moving to Southern NH.

If your car is reliable and has AWD then you should be OK with good all season tires, just keep an eye on your tread. If you have a FWD only car then def look into winter tires. Don't drive in a storm if you can avoid it. It's not like its snowing 24/7 in winter, we really only get a handful of big storms usually and you def know about them at least a day or two in advanced.

Check the weather before you leave the house. Weather in NH is nowhere near as predictable as SoCal so its a good habit year round.

Don't be too put off by your first winter here. Winter can def be rough especially moving from a perpetually sunny place but it brings its own fun. Try to get into winter sports/activities and it will def help stave off some of the seasonal depression. Ski/Snowboarding, Crosscountry skiing, Snowshoeing, Snow Mobiling... theres something for everyone and it can help you make new friends.

NH is a beautiful place. Enjoy.