From what I remember: feeding deer hay or straw during the winter can starve deer because they guorge themselves on it. This food source holds little nutritional value in comparison to natural browse. Therefore there is peer reveiwed sources stating deer have been found dead with a full stomach of hay/straw.
Chickens don't eat straw - although they will pick the seeds or chaff or whatever it's called out of it . And straw is SO much less dusty than shavings and drier than hay so it doesn't mold .and it's soft for the ducks and geese to sleep on, the chickens to walk on.