Archaeoptryx is not an example of a transitional fossil. It had fully formed feathers, its brain was like that of a flying animal, and its skeleal and muscular structure was fully developed for flight. That is not transitional.
Actually, the story told about the evolution of the horse is just that. A story. There is no gradual change from the little 4 toed creature of 50 million years ago to the horse we know today. The truth is that instead of gradual change, the fossils for each "intermediate species" appear fully distinct, exist for a time, and go extinct. This does not represent transition.
In terms of evolution – that does represent transition – a gradual change from a browsing creature of the woods to a grass eating plains running animal. Because it is “transitional” does not mean it each one is not a fully distinct species. Perhaps we need to define what transitional means because there are different types of transitional fossils.
First – there is "General lineage". This is a sequence of similar genera or families, linking an older group to a very different younger group. Each step in the sequence consists of some fossils that represent a certain genus or family, and the whole sequence often covers a span of tens of millions of years. A lineage like this shows obvious morphological intermediates for every major structural change, and the fossils occur roughly (but often not exactly) in the expected order. Usually there are still gaps between each of the groups -- few or none of the speciation events (the process by which new biological species arise) are preserved. Sometimes the individual specimens are not thought to be directly ancestral to the next-youngest fossils (i.e., they may be "cousins" or "uncles" rather than "parents"). However, they are assumed to be closely related to the actual ancestor, since they have intermediate morphology compared to the next-oldest and next-youngest "links".
The major point of these general lineages is that animals with intermediate morphology existed at the appropriate times, and thus that the transitions from the proposed ancestors are fully plausible.
Second – there is "Species-to-species transition". This is a set of numerous individual fossils that show a change between one species and another. It's a very fine-grained sequence documenting the actual speciation event, usually covering less than a million years. These species-to-species transitions are unmistakable when they are found. Throughout successive strata you see the population averages of teeth, feet, vertebrae, etc., changing from what is typical of the first species to what is typical of the next species.
Sometimes, these sequences occur only in a limited geographic area (the place where the speciation actually occurred), with analyses from any other area showing an apparently "sudden" change. Other times, though, the transition can be seen over a very wide geological area. Many "species-to-species transitions" are known, mostly for marine invertebrates and recent mammals (both those groups tend to have good fossil records), though they are not as abundant as the general .
Another point to consider is transitions to New Higher Taxa. Both types of transitions often result in a new "higher taxon" (a new genus, family, order, etc.) from a species belonging to a different, older taxon. There is nothing magical about this. The first members of the new group are not bizarre, chimeric animals; they are simply a new, slightly different species, barely different from the parent species. Eventually they give rise to a more different species, which in turn gives rise to a still more different species, and so on, until the descendents are radically different from the original parent stock. For example, the Order Perissodactyla (horses, etc.) and the Order Cetacea (whales) can both be traced back to early Eocene animals that looked only marginally different from each other, and didn't look at all like horses or whales. (They looked rather like small, dumb foxes with raccoon-like feet and simple teeth.) But over the following tens of millions of years, the descendents of those animals became more and more different, and now we call them two different orders.
Source for the above information is Talk Origins Archive.
Paleontologist Colin Patterson, director of the Natural History Museum in London, where "evolution of the horse" "transitional fossils" were on public display at that time on the ground floor of the museum, said the following about the exhibition:
"There have been an awful lot of stories, some more imaginative than others, about what the nature of that history [of life] really is. The most famous example, still on exhibit downstairs, is the exhibit on horse evolution prepared perhaps fifty years ago. That has been presented as the literal truth in textbook after textbook. Now I think that is lamentable, particularly when the people who propose those kinds of stories may themselves be aware of the speculative nature of some of that stuff."
The evolution of the horse scenario has been fabricated by using sequential arrangement of fossils of distinct species that lived at vastly different periods in India, South Africa, North America, and Europe, to present what evolutionist wish they could prove. There are more than 20 charts of the evolution of the horse, which, by the way, are completely different from each other. Each has been proposed by various researchers. It is clear that evolutionists still have reached no common agreement on these family trees. The only common feature in these arrangements is the belief that a dog-sized creature called eohippus (hyracotherium), which lived in the Eocene period 55 million years ago, was the ancestor of the horse. Those evolutionists ignore the fact, however, that eohippus is nearly identical to the hyrax, a small rabbit-like animal which still lives in Africa and has no relation whatsoever to the horse.
The imaginary line from Eohippus to Equus is very erratic to say the very least. It is alleged to show a continual increase in size, but the truth is that several variants were smaller than Eohippus, not larger. It is possible to bring specimens from different sources together in a convincing-looking sequence, but there is simply no evidence that they were actually ranged in this order in time.
I agree with what you say about the evolution of the horse – except, it does not in any way contradict evolution and that’s the issue. And also keep in mind - it is not only fossil evidence that is used to make these determinations but evidence from a host of other fields. Evolution is a fact – the exact mechanisms and details are still being explored but nothing you say above disputes evolution itself. Since then 1870, when Othniel Marsh first put together what he believed was the sequence of equine evolution the the number of equid fossils has increased dramatically, changing the overall evolutionary picture.
Yes - the actual evolutionary progression from Hyracotherium to Equus has been discovered to be much more complex and multi-branched than was initially supposed and the straight, direct progression from the former to the latter has been replaced by a more elaborate model with numerous branches in different directions, of which the modern horse is only one of many.
Yes - the change in equids' traits was also not always a "straight line" from Hyracotherium to Equus: some traits reversed themselves at various points in the evolution of new equid species, such as size and the presence of fossoles, and it is only in retrospect that certain evolutionary trends can be recognized
Fossil evidence suggests that the progression between species was not as smooth and consistent as was once believed – there I agree with you. However - some transitions, such as that of Dinohippus to Equus, were indeed gradual progressions, others, such as that of Epihippus to Mesohippus, were relatively abrupt and sudden in geologic time, taking place over only a few million years. Again, that doesn’t disprove evolution but instead suggests a new theory: punctuated equilibrium.
Eventually, in 1951 George Simpson recognized that the modern horse was not the "goal" of the entire lineage of equids – and yes, this contradicted modern evolutionary theory at the time. Simpson felt that Equus was simply the only genus of the many horse lineages that has happened to survive. This still doesn’t disprove evolution nor does it put a diety in the loop – it merely changes the details of the picture. People tend to jump on this as “proof” that evolution if weak, and that very weakness in turn provides “proof” that ID is valid. It doesn’t.