I'm Australian too, and a non-skier. I have spent time in the Swiss Alps during winter on three occasions so far - twice in late December and once in February. February is colder, and there is more snow about.
At Christmas last year in Wengen, Grindelwald and Mürren, there was no snow in the villages, although it was still cold. There was snow on the surrounding mountains though.
Any mountain tops you are likely to visit will have heated indoor areas - restaurants, shops and viewing areas. However, it is good to be suitably dressed in order to enjoy spending time outdoors and making the most of the mountain-top experience.
Here are details of the sort of clothing I wear in winter in the Swiss Alps, in which I have remained warm and comfortable for long periods outdoors.
1. Thermal tops and leggings. I like the Heattech range available in UNIQLO stores. They are warm, very comfortable and inexpensive, and I much prefer them to the expensive thermal wear you get in bushwalking stores. They have "warm" and "extra warm" styles.
2. Polar fleece jacket with full length zip. I like the Altica 200 range from Kathmandu stores - they provide just the right level of warmth for me. Full-length zips enable you to open the jacket if you are feeling a bit too warm. They have zipped outside pockets and some inside pockets as well.
3. Down-filled jacket, from bushwalking/outdoor shops such as Kathmandu. Mine is 80% goose down. I prefer styles with zips that open from the bottom as well as the top, with removable hoods and zipped pockets. They are OK for short periods in falling snow, but are not waterproof enough for rainy conditions. In rain, I wear an inexpensive lightweight waterproof jacket over the top of the down jacket. Ski jackets are waterproof, but I find them too bulky and heavy for travelling around.
4. Heavyweight pure-wool hiking socks. I like Icebreaker.
5. Gore-Tex lined waterproof hiking shoes. I like the Scarpa Stratos GTX shoe, which has good traction, but is also suitable for everyday wear when travelling. I have also worn them in the tropics (Kakadu), so they are a good all-rounder shoe. I am currently into my second pair, and always keep a spare pair on hand in case they stop making them. That's how much I like them!!
6. Cap, scarf and gloves of course. I prefer polar fleece to wool for these, but have some fine woollen glove liners for particularly cold days. I also wear ankle and wrist warmers in extra-cold conditions.
I hope this gives you a few ideas for deciding what will be right for you. If you need to buy any winter wear, I would do so in the next few months, as the range of available styles, sizes etc will be greatly reduced once the winter months are over. You may already know that the bushwalking stores have regular sales, so I would keep an eye out for these to help keep costs down.