How color is passed on (if it is as at all) depends on what color and species you are trying to breed.
Heraldic Unicorns are only female, and Paaefarin are only male. So breeding horses from these species is not possible due to the lack of appropriate mates.
Most colors have what's called the "standard" color inheritance. This means that a foal has a 25% chance of being the sire's color, a 25% chance of being the dam's color. There is a chance the foal will be some other color similar to one of the parents' colors (such as a Gold + Sealight may produce an Autumn), or a chance the foal will be a throwback to some unknown earlier ancestor.
There are a handful of colors that have % chance breeding. This means that the baby has a specific % chance of inheriting a parent's color. That chance might be anything from 1% to 99%.
This is a new, recently-discovered behavior. Horses that have color purity can be bred over generations to increase their color purity to 100%. When mated to other 100% pure horses of the same color they will always produce their color. All Color Purity foundation horses start at 4%. Their purebred offspring gain 3%-5% Color Purity each generation.
Color Purity horses will pass on 1/2 of their Color Purity to their same-colored offspring from impure matings. At 2% or less Color Purity the ability to pass on the color is lost.
These colors can only be bred 1x per season.
Color Purity horses cannot be inbred. "Inbred" means they share a common ancestor within the first 5 generations of their pedigree.
Horses that show a Color Purity stat on their page are from a Color Purity color.
Ethercorns might look like unicorns, but they're not really unicorns. Ethercorns are their own separate species with very unique color inheritance behavior.
"Pattern" is the hair marking (eg, Stripe1, Stripe2) or body marking (eg, Stripe1). "Color" is the color of the pattern. Manes, tails and bodies are all separate. This means you can have a horse with a Charcoal Stripe1 in their tail, a Currents Stripe1 in their mane and a Candy Stripe1 on their body.
The most important thing to know about Ethercorn breeding is that if you breed the exact same color and pattern on the exact same body part, the foal will have that color and pattern. For example: Mane Currents Stripe1 + Mane Currents Stripe1 will always produce Mane Currents Stripe1. However, Mane Currents Stripe1 and Tail Currents Stripe1 are totally different things.
Color inheritance operates on a ColorWheel. The closer two colors are together on the color wheel, the more predictable the breeding outcomes.
Each parent has a 50% chance of passing on their hair patterns. In the case of body patterns, there is a 12% chance if only one parent has that pattern, but a 100% chance if both parents have the same pattern.
If only one parent has a given pattern, and the foal inherits it, the resulting color will be calculated off the other parent's base color. For example: the sire has Mane Stripe 1 in Currents. The dam has no Mane Stripe1. The foal inherits Mane Stripe1. The foal's Mane Stripe1 color will be calculated off Currents (sire) and the dam's body color (eg, Candycorn)
All Bag-Born and Box-Born Ethercorns have 1-2 hair patterns in their Mane and 1-2 hair patterns in their tail. Bred Ethercorns may have all available patterns, or can be bred to be completely plain, with no patterns of any kind.