Horse breeders should learn this chant about their mares: "There are no due dates in horses....there are no due dates in horses...there are no due dates in horses." There is a RANGE of dates in which your mare could have her baby safely. For a mini perhaps 290 days forward, and one can certainly use 320 days in a mini as an average for those dates, but just because your mare goes OVER 320 days does not mean she is overdue. She may be taking her own sweet time (well..actually the baby is taking HIS own sweet time), but she is NOT overdue as there is no such thing.
In horses the foal determines the day of birth, that is when his lungs are mature enough and he starts emitting hormones into the mare's system which indicate to her body that the time is right. Once the mare receives this hormonal message, she can delay the actual delivery for up to 48-72 hours if necessary so that she delivers at a "safe" time when she feels secure and comfortable enough to put herself in that vulnerable position of being down and being in labor.
Humans on the other hand have lots of technology available to them which allows them to determine whether human babies are mature enough to be born, so induction of labor is not uncommon. Not so in the horse, so induction should only be considered when continued pregnancy endangers the health of the dam or for some other dire medical condition as determined by a veterinarian and NOT for the convenience of the owner. You've waited this long....what's another week or so. Sooner or later a baby will be forthcoming....though I do know how hard it is to wait to meet the little fella (as I am sitting here watching my own mare at 341 days!!!).