So, when you say "warm clothes" do you mean modern heat gear with synthetic insulators like 3M or do you mean before we learned to make clothes altogether? Because we learned to make clothes before we migrated out of Africa as far as we know.
One of the earliest remnants of clothing we have is Oetzi, the ice man. See here for photo. As you can see from the photo of the remnants of clothing that were found with him, early humans used hides and leather to make clothing and straw as insulation. Straw is a good insulator, especially combined with fur. The important thing in keeping warm is retaining body heat which we do by wearing layers that prevent the heat from escaping the air around us; by taking shelter in areas that keep warm air from escaping (aka a house); by warming the air around us with fire or heating. I'll talk a bit about clothing since I'm more familiar with that in a historical context.
The first thing to understand is that warm clothes have been a thing ever since we needed them. The most basic thing, of course, is animal skin in the form of fur and hides. We can see this clothing today in the traditional clothing of peoples of the North like the Inuit, or the Chukchi, or the Nganasan. Clearly, these are the clothes of those who live in areas where winter is the main season. What happens where we go further south? Well, you see more of the clothing made from woven fibers, mostly wool but also silk, and outfits made up of multiple layers with fur or hides present in the outer layers when possible. Let us look at the traditional clothing of Russia. It is made up of three distinct layers: the undershirt (rubaha), usually made of linen and multiple layers of which can be worn; the next layer made up of a dress (sarafan) or skirt (pon'ova) for women and a pair of pants (porti) for men; the outer clothes such as coats of all sorts, cloaks, mantles, etc which could be lined with wool. Hats were also a mandatory item both for social and for practical reasons. The key here is layering. The more layers you put on to prevent heat escaping the warmer you will be. Here is a picture of the different layers that someone in Russia (and Ukraine and Belarus) could have worn. The left most shows the basic outfit: pants, shirt, foot wraps and shoes (boots for the rich and nobility). Then you have the winter outfit of a merchant. Note the green fabric coat trimmed in fur with a fur coat covered in red (likely silk for a rich man) fabric on top. The next picture shows the indoor clothes of a noble, note how it still includes multiple layers with the orange coat and then the green overcoat. A poorer man would likely not have the overcoat and the materials that they were made of would be cheaper but you are still looking at multiple layers to keep you warm since there would still be the basic shirt and pants underneath. The rightmost picture shows the outfit of a bodyguard. Note the shorter coat with a wider skirt for ease of movement, but still edged with fur.
If we look at the clothing of the people of the Caucasus mountains and Central Asia we see similar elements to the clothing of Russians: for men pants, shirts, and loose long overcoats and robes; for women a shirt and then a combination of shirt, skirt, and overrobe, or shirt dress, and overrobe. Made of rich, heavy fabric, predominantly silk when possible or wool when not, these long, semi-loose layers would trap heat during the winter and could be switched for lighter equivalents during the summer. For some good illustration of the different layers of clothes in Central Asia I can suggest the manga Bride's Story which is fantastically researched and very accurately depicts the clothing worn in the region at the turn of the last century.
Something else that you see across the area is the use of scarves for women. As fashion tended to render women's clothes lighter, scarves were very useful in providing extra warmth in addition to being fashionable and religiously motivated. Here you can see a picture of two women in holiday outfits. Note the long dress overtop a shirt and the interesting short top worn on top of that. Called a dushegreya (translated as soul warmer) it was both a warmth layer as well as a fashion piece. As well, note the presence of scarves. The left picture has a young unmarried girl wearing one on her shoulders tucked into her dress while the married lady has hers on overtop her head and flowing past her shoulders. This was a very common way to wear a scarf and can still be seen in Russia today during the winter.
If you would like to see extant garments here is the link to the Russian Ethnographic Museum's online tour in which you can see examples of types of garments I have been speaking of in many different variations. This includes the costumes of Russia, Belarus, the Caucasus mountains and Central Asia, peoples of the north and also those of the Baltic.
Now, why have I talked about the clothing of Russians so much? One, because we have so many examples of extant traditional garments that were worn by people who did not have central heating and still had to survive very harsh winters. Two, these outfits have come down the centuries with mostly cosmetic changes so I could show real garments alongside pictures. Three, I wanted to show clothing from somewhere outside Western Europe.
A bit about housing: burning a fire or heating a stove inside a house or yurt or tent or any enclosed space, will keep you warm enough. Modern insulation just allows us to use less fuel and helps prevent drafts. In the past, as I hope I amply illustrated, you just worse more clothing that we tend to today.
Note: the links to sites or articles above are provided for the pictures not for the content of the articles, though the one of the history of the sarafan is interesting.
TL:DR Fur and layers. Just lots of fur and layers.
