I might have a work assignment in western WI starting around March next year. I've only ever lived in the South where it never snows, rarely freezes. How terrible will my experience be with the weather?

We usually have the last snow storm of the season in March, but the temps are usually moderate - nothing below 0.

The movie . Planes, trains and automobiles  comes  to mind. Steve Martin
The rental car desk scene.
" Your Fucked"

It's cold. REALLY  REALLY  COLD  !

????

PS
bring boiled peanuts & I'll  share my beer with you.
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There is often a significant difference in average winter weather from southern WI to northern WI. But there will definitely be miserable winter days throughout.

Not sure if this is helpful, but I'd rather live here in the cold than in south FL or TX or AZ.  My motto is: I can always put more clothes on, but there's only so much you want to see me take off!

Also, there's definitely something to acclimatization.   Up here the first spring day where the temps get to 40 degrees and we all shout "T-shirt weather!"  When I used to go to my Atlanta office they'd be wearing hats and gloves in 50's.

SW WI will be a lot easier during winter than NW WI. That said, it can run the gamut weather wise. Seen it here in So WI get to the mid 70's in early JANUARY and snow in May. Last winter we had a cold snap that hit -10F before windchills. Its not normal, but its possible to get extreme cold even in So WI.

Driving in snow is more of trying to be as smooth as possible on any control input and drive to your ability and comfort level. You'll get to see some rather idiot drivers in snow, especially the 1st real snow fall. Keep your vehicle in good condition mechanically. Keep supplies in your vehicle just in case. I keep an extra set of one of my hunting outfits (can handle well below zero) in the back of my truck along with ski goggles, flashlight, glow sticks, small plastic shovel and a blanket. I know some people who actually keep snow shoes.

My father is a born and raised Georgian. He moved up here in 79 and absolutely loves it. Winters up here aren't too bad(you've really got a 4 week window from late January-early February where it really sucks) and honestly i think a lot of it is mental. Just layer up and you'll be fine. Since you're coming up in March, you'll have plenty of time to learn what to wear and what not to. I think you'll be good to go.

Spring can be kind of a mess, moreso if it's been a snowy winter.

Depending on where in western WI you will be in what I consider the most beautiful part of this country.  The landscape is stunning in the driftless region.

don't listen to this lunatic.  That 4 week block is absolutely horrendous.  The month pre and post "aren't too bad," only in the 20s

Long sleeve shirt, sweatshirt or flannel, decent outer jacket.  Carhartt or similar if outdoors, something more hiking oriented (Columbia, North Face, etc) if not.  I lived in the south for a decade.... the first winter sucks.  Then you just grumble and accept it.  

The crazies up here insist there are winter sports.... but most people just need to keep warm between the door and their car.  

I'm sure all the native snow belt folks disagree with me.  But whatever, their reference frame isn't the same.  They think 70% humidity is Hades itself.