My husbands mare Fras hasn't been pregnant in almost 4 years. She will swell and drip milk whenever she comes into season. If your mare isn't bred than she may just be a "milk mare" like our Fras. We've talked about it with our vet and have decided to just live with it. The vet said we could try ReguMate if it bothered us but with the side effects and expense of the drug, we decided its no bother.
Just FYI, if the bag becomes hard, red and has heat to it, you need to have her checked for mastitis.
"Until one has loved an animal, part of one's soul remains unawakened..."
- Anatole France