Actually, I think I'm definitely going to guess that he got the silver from his daddy's side. If it's a long line of chestnuts, then it never would have shown up, but since his mom is black based, you got yourself a visibly silver baby. The light colouring on his legs right above his hooves in his more recent pictures is another good indication.
Just to update everyone. I had Bruno DNA tested and he is black! (a/a E+/e). He was also tested for cream, silver and gray and was negative for all three. Which means he's not silver, doesn't carry cream and won't gray out.
I was very surprised he was negative for silver, as I expected him to be positive for it. But, I was directed to a site that discussed "sabino roaning" by a member of another horse forum I participate in. The site said "sabino roaning" on a black based horse can be mistaken for silver dilution.
Another thing that makes me think it might be "sabino roaning" is he has little flecks throughout his coat (on his face, ears, neck and some on his body). They are small and you have to get up close to see them. But, according to this site (and several others I have visited) it along with his light/mane and tail is classic sign of sabino roaning. He probably inherited this from his dam, as she has one visibly classic sign of sabino, a "milk chin".
So, you are saying that as he matures his coat color will turn more of a black black rather than staying the chocolaty color that it is now? I have a mare (pictured in my avatar) and she is very black. If you were to stand Bruno and her side by side you can really tell the difference in their shades of black.