The Cŵn Annwfn are known primarily from the Mabinogi of Pwyll Pendefig Dyfed. In this tale, Pwyll departed his chief court of Arberth to go hunting in his favourite haunt of Glyn Cuch. One morning, as he set his dogs to the hunt he sounded his horn and began the hunt. Soon he had lost his companions, but he heard the barking of hounds other than his own. Coming to a glade he saw the hounds, beast with shining-white coats and blood-red ears, as they took down the stag. Chasing these dogs away he set his own hounds on the stag. But as he was doing this he saw a horseman approach upon a light-grey steed. The rider berates Pwyll for his discourtesy in setting his own hounds to a stag that had already been brought down. Pwyll offers to redeem himself of the stranger's friendship. The man tells Pwyll that he is Arawn from the realm of Annwfn. Arawn, of course, is the lord of the Cymric/Brythonic nether-realm of Annwfn (literally the un-deep) and his spectral hounds are the creatures and badges of his realm. In terms of attributes, the Cŵn Annwfn fall into the category of Celtic dogs that are associated with the realms of the dead.
In later folklore the Cŵn Annwfn became members of the spectral Wild Hunt. The wild hunt itself is a sectral procession of hounds and hunters led by the figure of Gwyn fab Nudd. The white-pelted red-eared hounds of annwfn became incorporated into the wild hunt. This may well be as a folkloric link was forged between Gwyn fab Nudd as a psychopomp and the hounds of Annwfn as netherworld creatures. This link was strengthened in folklore as the baying of the Cŵn Annwfn is meant to presage a future death.
If you would like to try the foods of the time of the ancient Celts, then why not have a look at the ancient recipes section of this site. For the foods of the time when some of these tales were written down, take a look at the Medieval recipes section of the site and, in particular, the recipes from The Forme of Cury.