I've been riding here in NYC for 5 years now. I've not had a bike stolen, but I have had some issues with locking. Ezdoesit's right about locking your wheels properly. I've been following the sheldon/missing link method for a while, but only locking the rear wheel inside the triangle. The problem is, however, that a lot of bike thieves are kind of stupid, and they don't get this renders the bike unsteal-able. They try by undoing the rear wheel quick release and then yanking on everything. The end result is a completely unusable and bent rim. If you lock both wheels together, it seems to work better for keeping people from messing with your bike at all--it just looks too formidable, and they're usually looking for a quick jack. However, to do that right, you need to have a bigger lock, which, to my mind, defeats the purpose. The skewers you have are fine. If I were you, I'd have a mini-U-lock, along with a cable lock. I've found the two-lock combination is very effective. It's not as intimidating or secure appearing as a burly chain, but it's a hell of a lot lighter, and along with the skewers, that gives you triple redundancy, which should be fine, especially if you're using the bike regularly (*the real problems with bike theft here come when you leave something around in one spot too long--after a few days, someone figures out you're bike's at least partially abandoned, and then it becomes their project and target. If you're NOT doing this, and riding your bike on a regular/daily basis, then with the basic locking strategies listed, you should be fine.) And, if that lot where you'll be parking your bike is secure, then you'll be golden.

As far as riding here in winter goes, December isn't such a bad month. It's often still in the 50s during the days right up until or even after Christmas, and any big snowfalls usually come after the New Year. However, you just never know. The big problem, though, is that after those early snowfalls, everything just gets piled up and then melts immediately because of the island heat effect. You end up having large mountains of icy, dirty slush, melting all over the streets. It's a disgusting mess, and coupled with NYC streets's poor drainage, you end up having huge puddles everywhere. If the cold temps happen to roll in, those puddles and wet spots all turn into ice everywhere. I'd say you should plan on, number one, wet weather. Have some things that will keep your feet dry. Also have wind protection. I'm assuming being from WI, that won't be a problem for you. As far as which of the bikes you listed above, I'd say go with the singlespeed MTB. Try and cover it up with some innertubes or something so it doesn't look so flashy, but that'll probably be the most useful for your purpose. (I think the folding bike will just get you wet and miserable really quickly; it also might interfere with your sight-lines at intersections, and that's not safe). Finally, as far as hauling stuff in traffic, well, people do everything here in traffic. You'll just need to navigate out the better streets. I recommend to people to ride on the left side on one-way streets--it makes you far more visible to drivers, and far less likely to be doored. If you ride on the right side, drivers will do whatever they can to inch by you, and sometimes, that means side-swiping you (I've had it happen to me several times). And with a big load, that makes it that much easier for you to take lanes when you need to, and generally be a more aggressive and visible rider. I don't think it will be a huge problem for you. I mean, basically, that's what the rickshaw guys here all do, and they ride all over traffic fearlessly. In fact, when you get here, I'd recommend you try and figure out common routes those guys use in traffic, and do the same. They're the ones riding around with a big haul all over this city.

Hope that helps, and good luck.

[edit] One last thing: Make sure you secure your saddle and seatpost. A simple bolt is often insufficient. Use an old chain and some innertube, or something equivalent. It doesn't matter what the parts actually are--dudes just love yanking those things and taking them home (I'm convinced a lot of bike thieves in the city are basically high school kids looking for a little fun).