What Color?

The sire side. Sire is bay/ dark brown and dam is black. Dam side sire is black and dam is chestnut with a flaxen mane and tail.

Brown does not equal looking chocolate. A brown horse can have a large percentage of completely black hair and still be a genetic brown. Your mare (who you said a few posts ago DOES sun fade) has the indicators of brown in the pictures, they are just hard to see because she is an unusually dark expression. The sire too looks like he is a really dark brown as opposed to a real black.

She turns like a smoky black color when she fades. She does not bleach like your typical black horse meaning turn red or brown. She does have palamino in her background but not a single brown horse in her entire 4 generation pedigree.

The foal is definitely brown- which means that either the sire or dam (or both) are actually brown, and not black. Since the foal is registered, parentage should have been verified, so that rules out the sire not actually being the sire.

From the pictures, it's a toss up as to who's brown and who's black with them. Stallion owners will often have their horses genetically color tested since people often want to know the color genetics before selecting a stallion to breed to, so you could check with them if they did an agouti test and not just the extension (black) test. You could easily test your mare as well; you just pull a few mane hairs and send them in with $25: link

Principal Investment, the stallion's sire, is a brown (looking at photos on google) not a bay.

I love a bad ass brown with tons of white! Congratulations!

I really wish I had a picture of the brown mare at the farm. She looks completely black with the brown/tan muzzle. Favor is brown, no doubt about it. My boy is also brown, but he looks bay. Browns are like chameleons XD

Bay is dominate over brown and red based horses can carry brown and bay and not have it be visible due to the lack of black pigment to work with.

Just a sort of off topic question; bay and brown are caused by the same thing correct? Black horse with agouti?
If so, then is it correct to say that browns are just very dark versions of bay, where the black has not been restricted to such an extreme degree?

Bay, brown and wild bay are forms of agouti.