Many nutritionists/scientists/vets consider hair testing for overall nutrient balance pointless. Nutritionists can't use results for balancing or consider hair testing credible in the face of such significant research.
Hair can be analysed for a variety of substances, including drugs, but in nutritional terms hair analysis refers to hair mineral levels. Minerals reach hair via the blood so it's going have the same limitations as blood testing since hormones control the levels of many of the minerals giving little indication of the status for the rest of the body.
The kidneys will rapidly excrete minerals when they are higher than a tight range, electrolytes like potassium are a good example. The liver can remove minerals before they reach hair.
It can't tell mineral balance even if the totals were credible as it doesn't indicate whether it's due to a deficiency in the first place or competition with another mineral or the body had a high need at that time. Hair can be useful for some heavy metals and selenium but from a nutrition point of view hair testing is pointless. This article by Dr Sarah Ralston VMD (Rutgers University) is about the limitations of blood testing but since hair is supplied by blood, it's relevant: http://esc.rutgers.edu/fact_sheet/diagnosis-of-nutritional-problems-in-horses/
There's been many studies which have demonstrated that many factors other than diet affect the mineral concentrations in hair. Things that affect the mineral levels in hair testing include the time of year, location on the body (different parts of the body test differently, even if they are the same hair colour), breed, age, hair colour, shampoo residues, airborne contamination, sweat, dust on the horse, soil on the horse (even if the horse looks clean), all make a difference. It's not uncommon for hair mineral analyses can't tell the difference between minerals that are on the surface of the hair and those that are actually inside the hair.
One study found higher concentrations of zinc in different colours of hair on the same animal. The same colour hair on different breeds of cattle eating the same food and in the same paddocks produced different mineral levels. Researchers found the age of calves/cows in the same paddock eating the same feed tested for different levels of minerals. Researchers found differences in mineral content of calf hair in calves by different sires - calves were all together and being fed same food.
Animals tested all year round showed different mineral level at different times of year, even though they were eating the same thing. There has been more success with hair testing for arsenic and cadmium, but even such things as age, sex, and length of hair, have been demonstrated to affect the testing for arsenic.
There is a huge body of research on hair analysis, and not one scientific paper has found any evidence that it is in any way effective for balancing the intake (that I know of). One vet researcher sent hair from one horse as separate samples and got very different results. If you know of a study and have a link, I'd love to read it.
Dr Eleanor Kellon discusses the limitations of hair testing in NRCPlus and Dr Ann Nyland researched this in great detail in her book 'Natural Horse Care The Right Way' if you'd like to read this great book: https://www.smashwords.com/books/view/33977
The best and most accurate approach is to have the intake tested (pasture/hay and so forth) and the diet balanced. Soil testing is valuable for long term soil treatment and improving pastures but not useful for determining what is in your horse's intake. Read more about soil testing...
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Dr Ann Nyland 2009 Natural horse care the right way, Chapter 3 Soil testing and hair analysis
Dr Eleanor Kellon VMD NRCPlus, Chapter 2 Tools