Is undyed wooI warmer than dyed wool?

Short answer: Most of the time:  No.

On a cloudy day in Ireland, the difference is detectable, with dyed being warmer.  Here in California, the difference is huge. On a cloudy night, there is little difference. On a clear cold night, then white wool is warmer.

I put a lot of effort into looking at the research on the topic a couple of years ago, and I have written about it before e.g., http://gansey.blogspot.com/2008/07/knitting-warm-woolens.html

I knit hundreds of swatches and tested their thermal properties. I started by making a little blower and blowing air through the samples and measuring air flow. I tested the samples for radiation absorption, transmission, and emission. And, I tested for conduction. I made holders (bras) for the fabric samples and compared "skin feeling". I knit entire garments in natural yarn, measured their warmth, then dyed them and remeasured their warmth. I knit similar garments from dyed yarn and undyed yarn. Then, I went walking in the rain changing sweaters every 15 minutes. I went downhill skiing, and changed my sweater after every run.

My results were similar to those developed years earlier by the US 10th Army, US Army Cold Weather Research Lab (at Aberdeen Proving Ground,HTTP://www.army.mil/info/organization/apg/), Gerry Cunningham, and Holubar Mountain Sport.

The primary path of heat loss through fabric is heat advection via air flow and water vapor. Air molecules and water vapor molecules are tiny compared to the distance between wool fibers in an ordinary knit fabric. Thus, most of the air and water vapor molecules moving through the fabric do not directly interact with the wool fibers in any way. Small changes in the surface of the fiber as a result of dying *do not* affect heat advection through the fabric. Larger changes in surface texture as a result of "super-wash" treatments have a small effect (allow increased flow/ reduced warmth of the fabric).

Small changes in the surface of the fibers *do* affect the ability of  liquid water to move from the outside surface of the fabric to the inside surface of the fabric. This is because there are hydrophilic sites on the wool fibers, and many dyes bind to these hydrophilic sites, and then the dye molecule presents a hydrophobic tail to any liquid water that contacts it. The presence of these hydrophobic tails tends to prevent water from wetting the wool fibers. Then, the water under its own surface tension forms a droplet. Motion in the fabric then tends to push these droplets outward, where they are able to drop off the fabric. The practical effect is to make fabric more weatherproof and warmer.

Water vapor passing from the inside to the outside of the knit fabric tends to condense on the outer surface of the garment. A blue fabric will absorb more light energy, which slightly warms the surface of the fabric, thereby reducing condensation. At the latitude of Ireland on a cloudy day, the difference between a natural white wool sweater and a navy blue sweater amounts to 0.3 watt per meter^2 per hour. This does not sound like much but it is enough to keep the outer surface noticeably dryer and warmer. However, on a cold, clear night, the white sweater will emit less radiation, and its surface will be warmer and dryer. If worn under an oil skin, the oil skin controls radiation, and different colored sweaters have the same warmth.

If you can hold a sweater up to the light and see points of light through the sweater, then heat (IR radiation) from your body can travel through those same holes.

Conduction is mostly an issue in socks and the inside of mittens. Even tightly felted wool holds plenty of air to retard heat loss by conduction.

Bottom line: Sailor's "ganseys" were blue, because blue sweaters were a good bit warmer. Arans were not dyed because that was cheaper, and in the rainy areas where they fished, they wore an oil skin, therefore, the color of their sweater did not matter.

Shetlands and other primitives produced colored wools, that reduced the need for dying these wools. The fine fibers with a high scale count of these breeds allowed spinning yarns that trapped air. For example Shetland lace yarn was 3-ply at about the same grist as English 2-ply. Thus, even their lace yarns were warmer. In addition, the stranded knitting produced very warm fabrics.

It is worth noting that the fine wools are better at trapping air, but in modern useage the wool fibers are too far apart to be effective at trapping air. If you want to effectively trap air, the wool fibers should be about 40 microns apart. That is a much tighter fabric than anything modern knitters are accustomed to knitting. On the other hand, such a tightly knit fabric is too warm for modern heated environments.

I was Senior Scientist at the world's largest engineering firm. My physics and chemistry are excellent. I have served on ASTM technical committees developing standard testing procedures. I understand testing procedures.

How do I account for all of the anecdotes that undyed wool is warmer? Skin feel is a very tricky thing. It can be very accurate if one is doing many inter-comparisons over a short period of time (and logging them carefully). However, over periods of a few days, the quality of the comparisons falls off dramatically. And, it there is not diligent contemporaneous logging of results, then the memory is going top play tricks on the results. It would take an extraordinary body of work for me to disbelieve the physics and chemistry of the situation. It would take an extraordinary body of work for me to disbelieve the US Army on this topic. No, my work, the Army's research, Gerry Cunningham's work, and Mrs. Holubar's work all confirm the physics and chemistry of the situation.

I suggest that many samples of undyed wool contain traces of potassium salts of lanolin fatty acids that tend to bond with the hydrophilic sites on the wool fibers and which then present hydrophobic tails to liquid water. This would temporarily give these wools the same water transport properties as dyed wools.  However, lanolin is not a stable molecule.  It will oxidize, and the wool will lose this virtue. see for example http://journal.scconline.org/pdf/cc1966/cc017n03/p00157-p00169.pdf  

Moreover, it does not give them the same radiation absorption characteristics