Coat colour is the only aspect of the life appearance of the Holocene European wild horse that can be determined with a high degree of certainty thanks to studies examining the coat colour genotype of aDNA samples from wild horses.
A 2017 study found that the a allele on the Agouti locus, which originated in Iberia in the late Pleistocene and which causes a black phenotype on an E+/E+ genotype in non-dun horses, became increasingly common among European wild horses in the Holocene until it became the prevalent allele in the later Holocene [1]. This alone does not tell us the phenotype of the animals, because they could have either been black or black dun (also called grullo, mouse dun or blue dun). The question now is: was the late Holocene European wild horse black or black dun?
The Dun locus was resolved in 2015 [2]. It was found that there are three alleles on this locus in horses: dun D, which is wildtype and basal for all living Equus, wildtype non-dun d1 which dates back well into the Pleistocene, and the domestic non-dun d2.
The black allele was restricted to Europe, it was not found in Siberia so far [1]. The wildtype non-dun allele, on the other hand, was so far found only in Siberia [2]. This could lead us to conclude that there were no horses of a genotype a/a d1/d1, therefore being black. However, it must be considered that the Dun locus was so far only tested for Siberian wild horses, and not for European wild horses. I think it is well possible that there were horses with an a/ad1/d1 genotype, because genetics suggest that during the Pleistocene there was one large panmictic population of wild horses from the Pyrenees to Siberia [3], what makes it possible at least that the d1 allele was also found in European Pleistocene wild horses, which were the predecessors of European Holocene wild horses [4]. Furthermore, some cave paintings might depict non-dun wild horses, such as those at Lascaux, which clearly show black and blackish brown or dark brown horses among a large yellowish-brown horse. This must be viewed with caution, however, because the exact shade of a cave painting is always dependent on the pigments available to the artists and may not necessarily reflect the true colour of the animals. But so far, cave paintings proved to be rather accurate on horse colours. F.e. the leopard spotted horses illustrated at Pech Merle were found to be based on horses having that colour [5], and Ekain also shows black dun among bay dun horses. Therefore, I think it is well-possible that there were black wild horses at least during the Pleistocene.
This might have depended on another allele as well. Sponenberg & Bellone (2017) state that seal brown, which is a colour found in Exmoor ponies, can be caused by a black phenotype being diluted by the dominant pangare allele Pa+[6]. Pangare is a basal equine allele because all living wild equines have it, so it must have been the ancestral state in European wild horses as well and some cave paintings illustrate it very clearly. If seal brown is indeed caused by a black phenotype being diluted by pangare, the existence of black wild horses would depend on if the non-pangare allele panp was present in wild horses or not. So far, this has not been tested. I used to think that black suppresses pangare, also because black dun horses always have a dark head while they sometimes may have faint countershading on the body (and as foals sometimes have a white muzzle). The genetic background of seal brown should be tested to be sure.
Another clue could be historic evidence. There are several records describing free-ranging horses in Europe, and until recently it was unclear whether they were truly wild horses, feral horses or hybrids. A recent study confirmed that they were most likely hybrids of feral domestic horses and the native European wild horses. Go here for a summary of those records on these hybrid populations. What is striking is that black dun horses seem to dominate these reports. Black horses are mentioned only very rarely. Of course, the phenotype of hybrids is not very strong evidence, only a hint, as the domestic horse introgression likely has changed the frequency of the colour phenotypes present in the populations. But black dun is not very frequent among domestic horse breeds. Also, dun in general is less frequent than both non-dun alleles in domestic horses, so that it is unlikely that introgression from dun-coloured domestic horses turned an originally black wild population into a black dun hybrid population. Considering that non-dun is more frequent than dun in domestic horses, I do not think that introgression increased the frequency of dun in the wild population and instead assume that the population was originally dun in most of the individuals. If the original wild population was black, this colour probably would be mentioned much more frequently than black dun in those reports on the hybrids.
All in all, I think the evidence for late Holocene European wild horses being mostly black dun outweighs that for them being black. I think it is well possible that there were black wild horses, at least in the Pleistocene, but more research would have to be done. For example, Holocene European wild horse remains could be tested for the dun and non-dun alleles as much as for the pangare and non-pangare alleles, and the genetic background of seal brown should finally be confirmed.
Literature
[1] Sandoval-Castellanos et al.: Coat colour adaptation of post-glacial horses to increasing forest vegetation. 2017.
[2] Imsland et al.: Regulatory mutations in TBX3 disrupt asymmetric hair pigmentation that underlies Dun camouflage color in horses. 2015.
[3] Cieslak et al.: Origin and history of mitochondrial DNA lineages in domestic horses. 2011.
[4] Fages et al.: Tracking five millennia of horse management with extensive ancient genome time series. 2019.
[5] Pruvost et al.: Genotypes of predomestic horses match phenotypes painted in Paleolithic works of cave art. 2011.
[6] Sponenberg & Bellone: Equine color genetics. 2017.