So I'm going to tell you everything that I've studied myself and also learned from the awesome people on horse forum such as Chiilaa, Posiedon, and NdAppy among others. I have a biology degree so I have a pretty decent foundation in genetics so I LOVE learning about this stuff and I get taught more and more all the time!
Ok so your have to understand there are multitude of genes present in horses or people or any living thing both homozygous, heterozygous, dominant, and recessive. That tobiano horse that is homozygous for that color means that its offspring will without a doubt get one copy of that gene. But you have to look at what other color genes are present a bald apron face I'm assuming this horse has is frame. The APHA would classify this as Torvero which is a confusing term that shouldn't be used. Torvero means tobiano and some other Overo pattern. Like I said earlier tobiano doesn't make any face white markings which means that it has to have the overo white markings which are Frame, Sabino, and Splash. Frame and Splash are also the only two genes that make blue eyes except for in double diluted horses but that doesn't apply here. Now I'm assuming your guys know what homozygous and heterozygous mean. So a horse that is a frame carrier is heterozygous and when its bred to another frame carrier you get these possible progeny possibilities. 25% no frame inherited, 50% frame inherited (heterozygous), 25% LETHAL (homozygous). You can get these results with a punnett square but I won't go into that.
So punnett squares when trying to map out possible inherited genes can get pretty complicated when you start adding in multiple dominant and recessive genes. I'm going to over simplify this a lot but its gets my point across. But basically you have to think about of those progeny that inherited the frame. Lets say the foal inherits frame from one parent and a solid body non white gene from the other. If the solid color is recessive and frame is dominant the frame will show up on the coat and mask the solid color gene. But it can be the other way around if the solid color is dominant over frame then the frame doesn't show on the coat. But regardless in either case where it shows or not the horse still carries frame.
So to save myself some time I'm just going to copy the frame definition from wikipedia which basically says what I said and thensome and here it is.
The frame overo pattern is the most common of the three types of overo patterns recognized in the American Paint Horse breed. A frame overo horse appears to be any solid base color (bay, black, chestnut, etc.) with white irregular patches added, usually with a horizontal orientation. Markings are often of jagged shape rather than rounded, the white rarely crosses the back, the lower legs tend to be dark, and the tail is one color, usually dark. The head is often white or bald-faced, and blue eyes are not uncommon. The frame overo pattern usually behaves like a dominant gene, in that when frame overo horses are crossed on nonspotted horses, about half of the foals come out spotted. There are records of frame overos being produced by two nonspotted parents. There is a theory, however, that these "solid" horses simply may be horses with very minimal expression of overo genetics.
Frame coloring is controversial because it is associated with lethal white syndrome (OLWS or LWS), the equine version of Hirschprung disease. LWS occurs when a foal is homozygous for the Ile118Lys EDNRB mutation, which is considered by many researchers to be "usually responsible" for the frame overo phenotype. However, other researchers emphasize that overo spotting patterns are phenotypically and genetically heterogeneous, that is, may have multiple sources. The frame overo gene can be masked by other white patterns, particularly tobiano, which is a dominant gene and epistatic to overo.
 Epistatic means that when both genes are present, this is the one expressed.
In addition, some carriers of the LWS allele appear to be solid. One theory holds that such horses carry the frame gene, but so minimal in expression that they appear solid. Either way, all LWS foals have horses with frame overo patterning in their pedigrees, and horses carrying a frame allele may not necessarily have a visible expression of the frame overo color.
The reason I said that mare is most like frame is the irregular shaped blaze that mare has and how the white reaches towards the eye especially on the side with the blue eye. It's very reminiscent of my friends mare who just had an OWLS foal because like your cousin she was horribly misinformed about frame. My friend AQHA mare has no white except for a small white spot on her side and her irregular shaped blaze. Frame is not restricted to paints its in several breeds.
Here is my friends mare.