Annette,
Boy you picked a big one!
The short answer would yes and no. But I will give you the correct answer. (Deep Breath)
To answer fully your question I need to take into account all 4 possible types I have characterized so far, however there could be more types than these or one of these types could be a combination of two of the four types. Please keep that in mind.
Unfortunately, I do not have my reference pictures on a website so I cannot show them here, and they need to stay off of websites for now, until I can definitively state such differences.
The carriers of types 1 and 4 SOMETIMES show subtle features of a type 1 dwarf, i.e. extremely domed forehead, large prominant eyes, very exotic head overall. That being said however, it is NOT 100% true. In the carriers of types 1 and 4, height is extremely variable, bone structure and thickness extremely variable, length of neck extremely variable. I have samples of parents that produce a type 1 dwarf that really do not show signs in the head and are not very small in height, the only give away was pedigree. However other samples give all of the signs, head, off mouth (usually underbite), build, height, and pedigree.
To clarify 1 vs. 4, the type 1 is the type we see most often, the type 4 is the lethal type that does not go to term.
Carriers of types 2 and 3 so far have shown no signs of being carriers, all so far show extreme variation in height and conformation, the only commonality in structure of the parents so far are overall head structure. They are straight, slightly large for body size, very normal looking heads you would see on a regular horse and ARE NOT exotic. But, they are NOT a straight pony head, i.e. what most people refer to in the pony breed. These characteristics are very general visual differences and commonalities I have experienced and documented, and are not conformational facts describing the disease carriers. They are only observations so far that I see as commonalities with conditions producing a dwarf.
Type 2 dwarf is the type that looks like it has a normal body neck and a large plain or straight head, the dwarf just looks like it had it legs cut in half, in reality the upper leg bones are severely shortened, hips miss-shaped, and a large head. These are the bones and structures that I can tell so far are affected, though I do not have enough samples x-rayed and compared to make that definitive. Unfortunately, this is the type I have seen in the past most often used in breeding progams due to the fact that they still have a mostly normal life and reproductive viability.
Type 3 dwarf is the most severe type that is viable, they are extremely small usually, have severe spine (roachback) and leg deformities, usually severely shortened neck, and severely deformed head with off bite. This type is possibly a combination of types, i.e. inheritance of two different recessive dwarf genes due to the fact that the bodies are so severely deformed and variable it has been very difficult to find a consistent deformed type.
There are some concepts I need to explain about the inheritance and expression of recessive genes to qualify my answers. This is especially important involving carriers of recessive dwarf genes and other recessive deleterious genes, and determining, visually, carriers or non carriers and the problems in doing only that.
One concept is PENETRANCE of a recessive gene over a dominant gene in a population. For example how a recessive dwarf gene's characteristics can penetrate and express the condition over the dominant normal gene's characteristics over a large population. Visual example is a normal horse that is a recessive carrier of the type 1 dwarfism and shows some of the characteristics individually or in combinations, like a severely domed head, very large eyes, under bite, etc. The strict genetic definition is "the frequency, under given environmental conditions, with which a specific phenotype is expressed by those individuals with a specific genotype." So you would see variable PENETRANCE of this recessive gene in the Miniature population, which is what I believe is occuring.
Another concept is EXPRESSIVITY of a recessive gene in one animal. The strict definition is the degree to which an expressed gene produces its effects in an organism. So if you take the example of the situation I explained with Penetrance, you have a normal carrier of a type 1 recessive dwarf gene, and it shows some characteristics of possibly being a carrier, well EXPRESSIVITY is the how much effect is the dwarf gene having on the individual horse to overpower the dominant gene, i.e. slang terminology one might hear is "How dwarfy does the horse look?"
Now you also need to understand the difference of these terms and concepts regarding recessive genes when comparing them to co-dominant genes. A co-dominant diseased gene would ALWAYS be expressed in a carrier with its normal counterpart in equal amounts and NEVER be "hidden". A good example in some flowers is the color pink, it is not a one color but a combination of different colored cells, some are red and come are white, making the color look pink with the naked eye.
If this is a little confusing, you can start another thread referring to this one.
John