Was the foal stillborn? I have not seen this in foals, but have seen feet like that on baby goats that were still born and believed to have died in utero some days before, early stages of tissue breakdown is what we always chalked it up to. Hopefully someone more experienced will have better ideas, I'll be interested to see the responses on here.
I'm very sorry for your loss.
From what little I can remember from my breeding books... foal hooves look like that in the last stages of development. They have soft caps on their hooves, and they're not solid so they won't damage the mare while they're being born. I can't remember what stage that is though... and I wish I could give you more solid information.
Very sorry about your loss. It's always really sad to lose a baby. Newborn foals are born with those little fingers on their feet. They don't have that many of them, but if you look at them when they are first born, they have a few on there. They are really soft, so that as soon as they try to stand, they start rubbing them off.
The rubbery sort of fluffy 'stuff' on the bottoms of newborn foal feet are sometimes called 'fairy slippers', among other nicknames-- as Justdressageit said, it is normal and it helps the foal pass thru the mare's reproductive tract without sharp hoof edges catching on either the inside of the mare or the amnion. It crumbles off as baby learns to stand. Some foals will have more or less-- this baby had a bit more than some foals do but still totally normal.