I've been trying to breed my chickens for a few in-game days now and nothing is happening. I have a rooster and two hens in the same coop. Do I need a specific building or item to start the breeding process? I saw something about a Selective Breeding House on the wiki but I'm not sure if that's required or just for advanced stuff.
Also, do different color variants matter for genetics? I have a white hen and a brown hen and I'm curious if the chick color is random or based on the parents.
You need the Selective Breeding House, which you unlock at the Intermediate Rancher certification with Pastelle. Once you have it, place a male and female of the same species inside and wait 3 in-game days. The genetics system is actually pretty deep. Color is inherited from both parents with some randomness, and there's a DNA trait system with traits like Workaholic, Twins, Precocial, Strong, Optimism, and Bulkiness that get passed down. There are also negative traits like Pride and Petiteness to breed out.
Adding to what was said above: the White Horse is a Senior Rancher tier unlock, so you'll need to work your way through the Apprentice, Junior, and Intermediate certifications first. Make sure you're buying your parent stock from Pastelle at Green Pasture Ranch to get the best starting traits.