Gen 2+ Breeding Process
First, I start with this.

This is a list of the latest adopts, all of whom are unbred. I sort them by gender, and make sure I can view the ID numbers for each adopt.
Next, I list out the stallion ID numbers, and pick what mare they will be bred with. I also assign the IDs and genders of the foals.

So in this example, 297 (stallion) and 300 (mare) will be bred, resulting in 305 (stallion).
The numbers to the far right correspond to the adopts as I view them. Here's the pairings visually:

Next, I isolate the genes that are guaranteed:

Both parents carry the same genes in this example for all guaranteed results, but there is a second scenario where I can do this, where parent 1 is EE and parent 2 is ee, resulting in a guaranteed Ee for the offspring.
Next, I roll dice for the other genes, and finish the genotype for the foal:

Usually I only need two dice for this, a d6 and a d4. Anything that has two outcomes is rolled as odds dominant and evens recessive, and anything with four outcomes is rolled as such:
rnto x RNTO
RNrn 1
RNto 2
TOrn 3
TOto 4
Pretty basic way of doing it.
The next step is to plug these into Jennifer Hoffman's generator to get the phenotype:

I then google real examples of the coat in sections:
Silver Dapple Dun
Horse with Splash
and reference those images for the actual design.
And.... that's it.
I also roll a d5 for the mane and tail.