I really don't know what the big bales weigh. Looking back on my comment I should probably revise my estimate of weight quite a ways upward. And I don't know the actual size of the bales, the big square one are probably close to 4x4x8 foot and the big round ones are probably 5 to 7 foot in diameter and 8-10 foot long.
I can't imagine anyone wrapping a bale in plastic for normal over the year storage. The quality of the hay depends on the water content when bailed. Too much water and it molds and starts fires, too little water and the food value decreases. Outside hay stacks are often covered with tarps to keep the rain/snow from injecting too much moisture but the sides are also usually open to aid air circulation.
It is possible that bales could be wrapped in plastic for short term storage, transportation, or use.