Thank you for the replies. Some thoughts of my own in return...
On leather:
Leather was certainly known and in use for the era. We have archeological finds of various leather implements. And there are saga descriptions of leather having been used as a coat, even - at least in one case - of someone resisting sword blows with a coat of reindeer hide (Heimskringlasaga, by Snorri Sturluson).
There is also a single find of what are believed to be leather Roman-style cuirass: "Probably the leather cuirass was made in two parts - front and back - and held in place by the clasps and by a leather belt or harness." (Dress in Anglo-Saxon England, Owen-Crocker, p193). However, that find is Anglo-Saxon, not Scandinavian (although it is reasonable to assume trade). It's also part of a rather special burial, and therefore suspect. And it's a single find, without a duplication that I am aware of from the era and region. It's also a bit earlier than the "Viking age" as most people date it.
It's reasonable to believe many Vikings may have fought in leather, but that's more likely due to leathers having been worn as sea garments - protection from the sea, rain, and wind - than as armor. Leather most certainly DOES have an ablative effect against swords. The main reason we may not have found "leather armor" could be that it didn't exist - but that leather was worn in battle, because leather was worn as part of normal seafaring clothes.
Textiles:
Mord's quite right about the textiles available. I've also read theories that cotton was sometimes traded to the north, and treated there as a high value textile (although it was very cheap to the south, around Egypt). But for the most part, we're talking flax linen and wool for textiles.
The Scandinavians most certainly had weaving, and used both sorts of fiber for their weaves - both tablet and warp-weighted looms. (Owen-Crocker p284-290). Cloth was time consuming to produce, but not unduly so:
...in Scandinavia, the warp weighted loom, which was easily dismantled, was stored in a barn; when a blanket or garment was needed, the loom could be set up against the kitchen wall for the time required to weave it, perhaps a few days. (Owen-Crocker, p289)
I did a bit of experimental archeology to test the mettle of woven wool against a sword. I took one live steel reproduction of a viking era sword, one iron anvil, and one block of white pine laid on a concrete floor, a chunk of 8oz veg tanned leather, and one piece of woven wool.
Single or doubled, the wool was consistently split when laid on the anvil and struck with force by the sword blade. Wool against an unyielding surface seems to offer very little protection against a sharp blade.
The white pine laid on concrete offered different results. Single, the wool split in two blows out of five. Doubled, the wool split the top layer only once, and both layers not at all. In each case, divots of 1-3 mm were driven into the pine - not cuts, but indents caused by the force passing through the wool.
Skin, fat, and muscle tissue over most of the body is even more yielding than pine. It is therefore reasonable to assume that while a doubled shirt of wool would not stop broken bones, and might not stop cuts to the extremities or the skin above the ribs (where bones are nearer the surface), it likely would stop many cuts to more vital areas, such as the abdomen, kidneys, upper arms, and thighs. All of these are places where a cutting blow could kill.
Is it "armor" to wear two shirts when going into battle? Or perhaps to wear even a third layer? If the warrior did so in the hope of preventing some injuries, then I would say yes, it's a primitive and basic form of armor. It's also interesting to ponder what impact the oiled leather sea-coat would have when worn over two wool shirts.
To test that, I layered the leather over the doubled wool. Striking with the anvil under the subject, the leather split consistently with each strike, however, neither layer of wool underneath was damaged. The pine was even more noteworthy: with doubled wool under 8oz leather on the pine block,
I could not cut through the leather! I tried about ten solid, full force blows, and while I left marks and dents on the leather, I could not cut through it.
None of these defenses would do as much against a spear thrust, but shields are fairly good defenses against spears - far better defense against a spear than they are against axe or sword. But it's against the axe and sword that the textile and/or leather garments that we know were worn as day to day clothes would have had the greatest impact.
Based on the above findings, I feel fairly confident that textile and leather were both effective in defense against weapons of the era. I also feel confident that they were used - if for no other reason, it seems likely that the people who didn't bother taking off the clothes they wore when traveling by ship likely survived more battles than those who 'dressed down'! Our lack of surviving leather or cloth armor could well have more to do with our own preconceptions of what that armor should look like. Rather than seeking out hardened leather cuirasses and 14c style gambesons, I suspect when looking for the "armor" these people wore, we should look instead at the clothes they wore in daily living, which served then well against the weapons they faced.
Submitted for your analysis and thoughts,
Owyn