This can be self explanatory in some sense, but of course you have no clue (at least I assume so) of life in Sweden, how cold it can be, things that maybe you won't find there so I'll just share some of the things I would have liked to know.
Living in FL can be quite easy and light to shop for as one can get by with just flip-flops, shorts, a tank top, and maybe some shades, but Sweden can add a few lbs to the travel bag lol
I would definitely invest on some thermal clothing. Trust me, even if you won't be going to the mountains, it can get down to -30°C. For those in the US that's -22°F. I wouldn't worry so much about getting thermal long sleeves, because you can just layer with a shirt, sweatshirt or fleece and a thick winter jacket, but with pants it's a little different so definitely bring or buy two pairs of thermal pants.
You probably might be asking, what do Swedes wear for pants...at least I wondered because jeans don't seem too cold proof. Well, jeans are actually okay and if used along with thermal pants can actually turn into some adequate insulation. Several pairs of jeans, corteroid pants are also good, and probably to the contrary of common belief, warm pajama pants are not necessary at all, but if you want are definitely comfy to use around at home.
As far as jackets, you can get by with just a few. You'll be worrying the same things very often, but you wanna keep relatively light on the packing. I brought one thick winter(impermeable) jacket, one nice classy pea coat (for going out-gotta look nice- I bought one for $50 dollars really nice Nautica coat at Macy's during Thanksgiving Sale), a sports fleece jacket, and a warm wool hoodie available for cheap ($20) at Walmart; this has been plenty sufficient. Keep in mind, you can always buy clothes here and surprisingly so for cheap by going to some local second hand shop.
I am going on a skiing trip soon, but forgot my ski pants; lucky for me I found a really nice and insulated ski jacket and ski pants, both for $13 (All dollars are in USD).
A pair of long sleeves would be good, maybe some argyle sweatshirts, and maybe even a bathing suit in case you want to use a public indoor pool for exercise or use a Sauna (my apartment complex has one and the gym as well.
Other than that, bring whatever you want and can fit as far as clothes go. Don't pack too much!
Your really can bring anything, but you need to choose wisely, because shoes take up a lot of room and with the snow and bitter cold, you wanna make sure you are keeping those extremities as warm as possible. This is what I would reccomend:
One pair of sneakers or running shoes that you can use for running, working out, gym, or just for casual use, but these won't be any use if you'll be outside much.
One pair of shoes, maybe leather...I bought some $20 Perry Ellis shoes
kind of like these that are leather so can are good for any light rain or snow.
I also brought with me a pair of formal dress like shoes, but as boots that I use a lot to go out to bars and any formal setting. Also, good for the snow, but don't really keep out the cold.
If you have good snow boots or really find some cheap ones back home I would bring them if your limited space allows, but really I think you're better off buying some here. You can really find some cheap ones at a Secondhand Shop.
I'm not sure if all of the accommodations are the same, but at least where I live, in Råsatt, there are no sheets provided...there is a pillow however. You are also provided with furniture such as table, desk, chair, closet, shelves, and bed mattress.You are not allowed to use a sleeping bag and are forced to buy sheets. I fortunately, brought a blanket and light thing sheets as well as a cover for my pillow so I saved money on these items. Don't worry about bringing warm thick blankets or sheets; Sweden has very good heating systems and every room, even the bathroom, have their own heating units. Sometimes, you might even feel too warm.
Miscellaneous-Things that maybe you wouldn't think of
By now you should know it's going to be quite cold; cold and dry. Unlike the humid Florida, it will be quite dry and chap stick and hand cream come quite in handy. You're already in a new country where things are all different and bizarre, so why make it more difficult? Bring the deodorant you like to use and of course bring extras, toothpaste, contact solution if applicable, hand soap, shampoo, body soap/wash, cologne. You can of course buy these things here, but remember everything is more expensive in Sweden and this way you don't have the hassle of buying any more things.
Something you probably haven't thought of is a medicine kit. I don't mean a first aid kit with bandages and gauze pads (you can if you want to of course), but I am referring to advil, airborne...things that you would normally use but probably wont find when you get sick. I brought with me Airborne and Echinacea to strengthen your immune systems for colds and flu, advil for headaches and pain relief, Peptobismol is also good for a sudden upset stomach, and maybe even get some Antibiotics from your doctor before you leave. On that note, I would get a physical/general check up before you leave.
Of course you'll want to bring your laptop, some school supplies, a backpack for school (whatever it is you're used to using), of course all your documents such as passports, credit cards, ID's etc. Another thing you will maybe forget is some patriotic paraphernalia, whether a sports jersey or a flag because you will definitely want to proudly represent your country while here as there will plenty of events and cultural days.
Nowadays, we cannot live without a cellphone huh? Well, know that you could very well use yours here. The school should provide you with a free local Swedish SIM card offered through a company called Comviq that can allow you to use with prepaid credit.
I would look into unlocking your phone well before leaving, if you already haven't done it, so that you can use it here in Sweden.
I can probably help you out with unlocking it and especially if you have a blackberry since that's the phone I have. Here's a website that offers free unlock codes for blackberrys.
You can also bring a old phone maybe if you don't want to risk losing your new Android or iPhone but these need to be unlocked as well and most providers can offer these to you at no cost.
Worst case scenario, you can buy a cheap phone like this for $15-20
Don't forget to check your electronics for internal converters capable of handling 220-230V which is the standard in the EU. You will regardless need adapters and can find cheap ones from Amazon. Don't forget your chargers!!!
That's really all I can think of for now as to what to pack and bring with you.
Of course, don't forget your camera!!!