I know not a horse, but we are in the middle of calving, and the calves are tasting hay within just a day or two of birth; once they are about a week old, they are even more interested (still most of their diet is milk).
foals tend to drink small amounts often. I was worried about Dolly when she was born, Caddy didn't seem to have much of a bag; but Dolly was spunky, so I was told not to worry.
Here are Dolly pics from just a few days old, as you can see she came out chubby, and stayed chubby:
Birthday:
Two days old:
about two weeks old:
And about two months old:
I honestly don't rememeber when Dolly started tasting her dam's feed, but...
My APHA mare when she was born, her dam did seem to be short on milk and Hayley started really eating feed at only a few days old. I built her a creep feeder at about a week old. Vet had no problem with her eating mare/foal feed at such a young age. I think I started her on a cup or two 2x daily, and it didn't take her long to be eating a decent amount. She turned out just fine.
Mare and Foal on birthday:
Didn't have a digital camera back then, so few pics on computer.
Here's an adult pic of her, she matured just fine (she's 11 in this pic):