1. Dapples is a hidden recessive gene. For a horse to show dapples it must have 2 recessive genes. If a horse without dapples gives birth to a dappled foal you know the horse is carrying the gene. Likewise, dappled horses always pass one copy of the gene down. One thing you can look for is a horse with one dappled parent to breed to your dappled chinc. The foal will have a 50/50 chance of being a carrier or showing dapples.

2. Sooty is not hidden, you can do the gene test in the vet. Sooty is also dominant, so if a horse has the So gene it will always express it. If your horse has two copies (SoSo) they will always pass a copy onto their foals. If they have one (Soso) there is a 50/50 chance of the foal being sooty. 

3. No, Gray is dominant so in this instance the foal did not get the gray gene from its sire. 

Thank you so much Talitha!!

Talitha--so if we have a dappled horse that has a non-dappled foal, that foal would be a carrier? I'm just wondering if I need to note that in their name or something so I can remember who may have dapples.  Because they have a chance of throwing dapples themselves (if the horse they're being bred to is dappled or has a dappled parent) if I'm understanding that correctly.^_^

indigo what i do is add ^dappled if they are dappled and ^ndap if they are maybe a dappled carrier but  its a 50/50 chance for them to be a dapple carrier if u breed two horses that are ndap theres a chance for the foal to come out wirth dapples i use the foal predictor to check to see if a dappled foal comes out i pick one horse that is dappled and one that may be a dapple carrier just to check

Thank you, Hakken! I appreciate that. I will have to start using the foal predictor more, lol.