Foxes mate in the winter. It may have been a vixen calling, but have you thought about the possibility it may have been a big cat, as in panther? I would imagine your goats will see plenty of foxes and would be unlikely to display such an extreme reaction to one.
There is, it's said, a big cat around Glenrothes, Balbirnie Park has been the site of repeated sightings. Not so far from you.
We have a large black cat around here. It's been seen by quite a lot of people, including my wife.