Let's begin with a little logic issue. Scandinavia is a cold place. Many humans like a hat when living in a cold place. Viking Age people were living in houses made of wood, with thatched or turf roofs, a hole for smoke to go out, and a central fire. That is going to be cold in the winter. There are several types of hats or hairnets from before the Viking Age from bog bodies.
Lots of hats: http://nvg.org.au/article.php?story=2008032806363487
So, we know it was cold.
We know that the technology to make a hat existed.
Next up is the social expectation of wearing a hat. The Valkyrie figures appear to be wearing their hair knotted on top of their head. They are also often wearing what we think are ceremonial clothes (front panels, trains, etc). I don't think that most women, when cooking in the fire and doing other daily activities, dressed in this manner everyday.
This one...no hat.
This one might be wearing a hat....
There are a variety of hats, veils, scarves, and other head coverings found from the Viking Age. Most of them were not found in mainland Scandinavia. Please see "Viking Age Headcoverings from Dublin" for most of them. http://www.amazon.com/Viking-Headcoverings-Dublin-Medieval-Excavations/dp/0954385551
http://www.olvikthing.org/wp-content/uploads/2012/07/Viking-Age-Clothing-pgs-31-34.pdf
There is a similar hat found at York, http://www.historyofyork.org.uk/timeline/viking/viking-silk-cap
In addition, there are veils found in at least two burials in Scandinavia
http://as.tirrigh.org/files/Viking-AgeHeaddresswTabletWovenBand.pdf
http://www.nnu.dk/makro/Kong%20Haralds%20voelve.pdf
Now we have a pile of possible garments to be worn on the head.
(Fur trimmed pieced hats are going to get their own post)
1. Little "coifs", either rectangular or with a rounded point
2. Scarf-things, in various shapes and sizes, with or without trim or fringe
3. Headband/fillet things
We really have no idea how these were worn.
One at a time? In combinations? All at once?
NOW COMES THE EXPERIMENTAL PART.
We were getting dressed for a very cold expedition one day. I was thinking of wearing my paneled hat with a fur band, but honestly, there isn't a ton of evidence for that, especially for a woman wearing it. I was thinking about the reconstructions in the Dublin book, which I had somehow only considered with linen and silk components. I suddenly realized that most of those components come in wool too! I grabbed my little linen "coif" thing, then put my big, fine wool veil over that, and tied it on with one of my narrow woven belts.
Huh.
That is really sturdy.
And really WARM.
HUH!
This also looks a lot like the lumpy-headed (and sometimes you can see another color under them) Byzantine veil things. HUH.
(from here: http://www.medievalwall.com/cultural-history/medieval-clothing/)
Well. That was an awesome experiment, but the big veil wound around my neck is really warm, but not super practical for my usual everyday life. Then I started thinking about the size of veils. I also didn't like where I tied the band over the top. So I tried a couple more possible arrangements. And I found one that I REALLY LIKE.
Okay, let's take a break for a second, and reiterate. The following is one hypothesis, many others are equally possible.
WE HAVE NO IDEA WHAT VIKING AGE SCANDINAVIAN WOMEN WORE ON THEIR HEAD.
The following hat arrangement is made out of layers that are plausible, or were found in the Viking Age.
My hat arrangement is
A. comfortable
B. plausible
C. won't fall off (I slept in it, ran around, I'd be confident wrestling in this hat)
D. made of things that would be cheap and/or easy to obtain (one bit of linen folded in half and sewed into a square with ties, one square of thin wool, one band (should be tablet woven, I couldn't find mine so I used a little strip of brown linen)
Here is how I arranged it:
Step 1.
Base layer
I used a square/pointy hat for this, but a wide band of linen would also work. The purpose of this layer is to make a tightly tied, not slippery, not itchy, and washable layer next to the skin.
Tie the hat tightly, with the front coming down a little over the forehead, and the ties at the base of the neck.
I should note that my hair is up in a bun on the back of my head, taped in place with ribbon.
Step 2.
Hat thing.
I used a bit of black wool just large enough to meet in the back, and just large enough to tuck in.
I put the fabric on my head with the ends at the base of my neck. If this has ties, or is large enough, it can just be tied. I attached mine by tying a bit of string around my head.
This is a silly hat.
Many of the Russian Viking Age reenactors wear a hat very like this
Step 3.
TUCKING! I tucked the ends of the fabric under the ties at the base of my neck. This takes a while to arrange in a flattering way. Have a friend help or use a mirror. It will start out really blocky and lumpy, keep pulling the big bits to the back and tucking more tightly.
Much more cute hat!
4.
Hlad/band/attachy-thingy
The step above will kinda stay, but isn't nearly as sturdy as if you add an additional band. I find that it is most sturdy if I put the band from the front of my forehead to the middle of my hair (my hair is taped up in a bun on the back of my head, remember).
I'm wearing a scrap of linen as the band in this photo, because I couldn't find my nice cardweaving (sigh).
Notes. I have a lot of earrings (visible in the first image). Having the bands over my ears is very uncomfortable, so I put the under-hat behind my ears, the string behind my ears, and the final band above my ears. You can arrange the black layer around your ears however you want. It can be very high up, or totally cover your ears if it is very cold.
This hat is WARM. WARM!!!
Is there proof this hat existed in Viking Age Scandinavia?
NO. ABSOLUTELY NOT.
Remember what section this is...we are pushing the envelope here, not doing things that are well supported by tons of good research. I think it is plausible, it is made up of plausible or well supported items, it works, and dang it, I like it :)
So, one new hat for me, your mileage may vary.
Here are a bunch of images that I found of either useful evidence OR other reenactors' reconstructions.
http://www.pinterest.com/gargoyal2/hats-and-haircoverings-from-the-viking-age/