My stepmom is from Florida and she has 0 regrets about living in NH. I asked her last weekend while we were in Florida for a funeral if she would ever want to get a second home in Florida and do the Snowbird thing, and she said never...

On the topic of what you should know... This is going to be long:

Drive slow in snow and if you feel yourself sliding pump the brakes like 5 times or so real fast and let your car slow down and regain traction. Do not slam on the brakes, make sudden turns, or accelerate through bad traction. This is something you will learn over time, much like how to regain traction while hydroplaning which I would imagine you've done before in Florida (obviously the pumping the brakes is a lot different but the "don't panic" mentality is the same)...

Get a heavy winter coat and a few hoodies and good insulated gloves. It's obviously a lot colder than Florida and you will hate yourself if you have to shovel snow with no nice gloves.

Keep a Ice Scraper/ snow brush in your car (I do year round as one time I took it out of the trunk and the snow came earlier than I had expected and I didn't have it that day which was annoying). There eventually will be a day where you feel like the character from the movie fargo scraping the ice off your windshield.

A shovel for your driveway / porch / deck

Waterproof boots, as the snow is often wet and slushy (it is currently super wet where I am)

Liquor is only sold at NH state liquor stores

Once winter ends the roads are typically f'd up from frost heaves, potholes, etc. Expect to have to take a detour every now and then come spring/summer as the road construction is basically an expectation on a yearly basis.

Also as you can tell already, NH, like Florida, is not free from dumb people... Most of us just ignore them.