Are you asking about whether the silver gene came from the POA side or the QH side? Silver dapple is commonly seen in Rocky Mountain Horses, but is definitely not restricted to them. I'm not sure about POA, but it is known to exist in quarter horses.
The silver gene only affects black hair, so if it did come from the QH half, it wouldn't have shown up on the chestnut QH sire. From your description of the dam, I'm really not sure if she was silver dapple or perhaps something like varnish roan. The tiny white spots you mention on her make me think she had varnish roan (which is common in POA) whether or not she also had silver.
Without pictures of the dam, it's purely speculation, however.