Splash Overo, as everyone has said, is a totally different gene than the Frame (Lethal White) Overo gene. Only two horses that carry the LWO gene, bred to each other, have any chance of producing a lethal white foal. But, if your horse comes from a pedigree with Frame horses, has any blue in its eyes, or any white markings that might indicate the presence of the LWO gene, then it is best to test them before breeding them to any other horse that has not been tested to be LWO negative.
Splash is believed to be an ‘incomplete’ dominant pattern gene. The way the pattern is expressed depends on whether the horse is homozygous or heterozygous for the gene. Think of it similar to the way that you do the ‘Cream’ gene expressing itself. With Cream, one gene on a red horse (heterozygous) will give you a palomino, but two genes (homozygous) will give you a cremello. In a similar way, with Splash, there is a difference in the expression of the pattern depending on whether the horse gets one or two copies of the gene.
The other pinto patterns are considered ‘simple’ dominants; they can be fully expressed even if the horse is only heterozygous for the gene. There isn’t any difference in the likelihood of a wild pattern in a tobiano whether the foal is heterozygous or homozygous for the tobiano gene. Both have the same chances for having a lot, or just a little bit of white.
Splash is different. To get the wild splash markings, the horse has to be homozygous for the pattern*. If a horse is only heterozygous for Splash, it should show some kind of Splash characteristic, but not necessarily the body white. Splash characteristics can be blue eyes (or even just a tiny bit of ice blue in one eye), white face markings (even just a few white hairs), or some white on the lower legs.
If you breed an obviously Splash horse to a TRUE ‘solid’, you aren’t likely to get an obviously Splash foal. The foal will only be heterozygous for Splash, so will only have the Splash characteristics, not the full pattern. To get the full pattern, both parents would have to have at least Splash characteristics, although neither of them would have to be wildly marked. The parents might even be considered to be ‘solid’ if a person wasn’t looking for the characteristics. In these cases, a person might be surprised at getting a wildly colored foal out of two supposedly ‘solid’ horses.
An obvious Splash bred to another Splash patterned horse should give you 100% patterned foals. When bred to a true solid it should have 100% foals with Splash characteristics. Bred to a horse with characteristics only, you would expect to have 50% Splash patterned foals and 50% that will have characteristics.
The amount of white that you get with the pattern is variable, from minimal to almost all white, just as it is variable with a heterozygous or homozygous tobiano pattern. There are other factors that determine the amount of white that is displayed. The Splash, Tobiano, or Frame genes just determine the way/location that the white displays.
The Splash gene interacts with other Pinto patterns to often add more white and can increase the ‘wildness’ of the pattern displayed. Splash tends to put white on the face and lower legs, so can give a tobiano a blaze or possibly put socks a frame overo. If you are familiar with the way that Splash places color/white, you can also see the Splash influence in the body patterns on a horse that is also displaying the tobiano and frame patterns.
* (Note: The percentages, etc. may not ALWAYS hold true, as there are nearly always exceptions to any rule, but for the most part, colors and patterns should produce according to the ‘rules’.)