Do cows eat potato plants

If you mean 'would cows eat their food in a field of potatoes', then yes, since the potatoes do not harass the cows, they would happily eat in a field of potatoes, chewing their cud.

If you mean 'would they eat what is in the field of potatoes', then really, no, since all they would eat is the grass surrounding the potatoes or the field. They would not eat the potatoes.

cows eat anything green...