Absolutely.

First, come and visit us during the winter. The best way to see exactly what you'll have to deal with is not by reading it in my blog (although that isn't a bad idea). It's by going on a tour when it's all nice and cold and snowy out. Usually, that means January or February.

Second, I believe that everyone is different. Everyone has different tolerances and some people can take things that other's can't. Some people need to bundle themselves up as much as possible when even the smallest flurry shows up. Some people stay in shorts and t-shirts all year long (really. I've seen it). I wouldn't recommend that for people from tropical climates, but it's an option.

However, I do believe that the following is always a good idea.

You should have a nice warm coat. You can really use anything you want, but a few that come to mind are Marmot, North Face, Merrell, something like that. I guarantee any ski or snowboard jacket would be fine. I prefer something with a hood of some sort, but that's really up to you. You definitely want something that will keep you warm, but also keep you dry at the same time.

You should also have boots. Flip flops and sandals are great, but they do nothing in the winter. Same with heels of any kind. Get some boots. Once again, it's whatever your comfortable with.
Wearer beware: you may fall down no matter what you wear, but I think it's much easier to do so in heels. I haven't actually done so myself, but I've seen ladies try it and some end up on their butt.

Heat escapes via the head pretty easily, so some would say a hat is required. Any hat would do, but I personally am not a hat person. I personally feel this part is optional.

I think gloves can be pretty useful. I have a pair of old gloves that I've used for years that work pretty well. You could use mittens as well if that's your thing. You could always just stick your hands in your pockets too.

That's all I can think of right now. I'm sure you could use all sorts of things, but what matters the most is what is most useful to you. If you aren't going to wear a hat, then don't buy a hat. If you can't stand wearing gloves, then don't wear them. It's all about what you are comfortable in. It that means you wear a hoodie, scarfs, or your entire ski outfit, then do it.

Although I wouldn't recommend going to class in your entire ski outfit. I think that might be a little bit overkill.
If you've got additional questions or need more about this, don't hesitate to ask. You know where to find me.