This depends on the animal and the type of weed. Rarely do animals prefer to eat noxious weeds. Most often on pastures infested with weeds, the animals will graze the desirable vegetation, causing an increase in the problem weeds.
Elk prefer native forbs and grasses and will starve to death on ranges infested with Spotted knapweed and Leafy spurge. Doves readily eat and distribute Leafy spurge seeds. Leafy spurge can be grazed by sheep, but is toxic to cattle and horses can eat Musk thistle blooms, while Russian knapweed is toxic to them.