There is no right or wrong timing for traveling, only wrong clothing worn at the wrong time. I find this saying to be true to some extent, as all seasons offer different scenes and experiences. In 2014, we visited New Zealand and South Korea during winter. New Zealand's winter is mild compares to South Korea. When we were in the South Island (which was colder than North Island) of New Zealand, we were OK with a good thermal wear and wind-proof jacket or wool sweater. But in Korea, we had to layer - a good thermal wear, a normal shirt, a good sweater and then a good jacket. We wrapped ourselves in layers, so that we could remove any layer quickly when we went indoor, just like peeling an onion. :D
This picture showed a little on how we layered for Baby Bear. She had her thermal wear (top and bottom), her normal shirt and jeans, a sweater with thick faux fur lining and lastly a down jacket. Her down jacket is by Converse, the quality is very good, which could withstand Seoul's -14 degree Celsius temperature with the right layering. :)
Thermal wear is one of the important winter gears. Beware of low grade thermal wear which is a complete waste of money and luggage space. Going with Uniqlo will be the safest, as its extra warm heat-tech thermal wear is thin, lightweight and very good in retaining heat. I'll recommend going straight for its extra warm collection if you can, so that you can use it in any other colder countries you plan to visit, instead of buying another set later on. We bought some thermal wear from Going Places. The quality is very good too but thicker compares to Uniqlo's heat-tech collection.
For babies or young toddlers, there's no other choice but to buy from shops like Going Places. Sometimes H&M might have the thermal wear for babies or you may try Taobao. :)
Next will be sweater. You may also consider fleece jacket as your second layer. If you prefer something lighter and thinner, wool tops will be a great choice. Papa Bear, Brother Bear and I wore wool tops as our second layer while we were in Korea, so that we didn't look like big fat potatoes. Those were lightweight, but worked well to keep us warm. Uniqlo and Going Places have a wide selections for both fleece jackets and wool tops. Price is fixed for Uniqlo, unless during its end of season sale. Going Places will often have discount up to 50%. So do check out the sale from time to time. :)
Sister Bear in her thermal wear (top and bottom) and a normal t-shirt and sweat pants from H&M. Picture taken at Queenstown, New Zealand, temperature was 4 degree Celsius.
It was colder in the evening at Queenstown, New Zealand, which the temperature was near 0 degree Celsius. She had to add a layer of sweater and cold hat over her thermal wear and normal clothing.
Woot... this picture brought us to the freezing chilly Korea. Neck scarf, ear mask, face mask, gloves, cold hat and whatever which could keep you warm are needed. :)
Then it will be your jacket, which is very important, as this is the one which will appear in all your travel pictures! Hehe... Papa Bear has been very kind to me that he will always offer to buy me at least one new jacket before or during our trip. He knows I'm vain. :P
For jackets, you have the choice of wearing a polyester filled or down feathers filled windproof jacket. These are lightweight and travel friendly. Down jackets could retain heat better and its price is much more expensive than polyester jackets. You could also consider a wool trench coat, which is stylish. It's my favourite when I travel overseas for work. My only complaint is that wool trench coat is heavier compares to down jacket.
Us dressing like big fat onions. :) Picture taken at Nami Island, temperature was -6 degree Celsius. Thank goodness for the fireplace. :)
Some other accessories you will need are cold hat, ear or even face mask for extremely cold winter, wool socks, water proof walking shoes or boots. You can buy these at the countries you are visiting if your itinerary upon arrival include a shopping trip, else it's good to buy from home. For example, when we arrived New Zealand and South Korea, we didn't have plan or time to shop until day 3 or 4 onwards. Those we saw from the souvenir shops are calling for tourist prices. So shop from home during sale could be much cheaper. So it really depends on your itinerary and plan.
The above are just my personal experiences. You may Googled and read more of what others are sharing or doing in preparation for a winter trip. Have fun planning! :)