I've been overwintering nucs for about 6 years now. I've been refining my method over the years.
My first attempt was keeping 5 frame wooden nucs in the basement with an entrance to the outside and fed sugar syrup.
The problem I had was that feeding syrup provided too much moisture and the bees suffered from dysentery.
The next year I added screened bottoms and screen vents in the top. Although this improved ventilation and reduced moisture, I still had issues with dysentery. Furthermore, the nucs got a real late start in the spring flying and building up. Basically the basement didn't warm up enough to entice them to fly on warm spring days.
I then progressed to moving them outside in the early spring and giving them some aux heat with a heat lamp. It still seemed that although they survived in the basement, they suffered from not taking any cleansing flight during the winter.
My latest process is to keep them outside all winter and provide aux heat from underneath with 7W night lights when the temperature falls below freezing. I also have moved away from syrup because of the dysentery and feed blocks of hard candy right on top of the frames. This allows the cluster to move right to the candy and not have to break cluster to go to a source above the inner cover. This seems to work quite well for me.
I only do this on a small scale (2 to 3 a year) and although the last 2 years were successful, they were also rather mild winters.
There shouldn't be any problem with polystyrene if you only feed hard candy.