Cutting frozen netting off of bales is no fun. Especially if the bottom of the bale is wet, making a rock hard area at the bottom. Even though it doesn't stay below freezing all winter here, a good cold spell can leave the bottoms of the bales frozen even after it warms up. I buy most of my hay, and when my supplier gave me an option, I went with sisal.
A few years ago, I got a piece of poly twine wrapped around my foot on a rainy night . Not too big a deal until my 2400 lb bull got the other end wrapped around his foot. Hopping along on one foot, in the mud, holding my flashlight under my arm, trying to reach the twine with my knife was nothing like fun, and I didn't really appreciate how dangerous it was and how stupid I was to let the situation get there until I was back in the house.
That said, I store about half of my round bales inside, and the other half in a three high pyramid stack with tarps. If I couldn't cover them, I'd go with net.