Astute observers will note that a wooden scaffold shaped like a cow typically does not allow one to mate with Bovinae. Clearly, something else — the will of the gods, maybe — was involved. Or maybe Daedalus was just that skilled.
However, some scholars think that Daedalus was not so skilled as to allow life where none should exist; he instead found the artifact known as the Daedalan Crucible and incorporated it into his design. (Some scholars further rant that the Daedalan Crucible has certain similarities with the crystal computer of the doom cave of Wiki Dot Pod. But who believes the sorts of sages to travel with wandering murderhobos, anyway?)
The Daedalan Crucible is a small object, roughly the same size and shape as a modern contraceptive diaphragm, It is shiny, flexible, and lightweight. Although it is too fine to be seen with the naked eye, the Daedalan Crucible is composed of a mesh, a crystal and metal latticework of unknown provenance and design. It operates best inserted into the reproductive organs of humanoid females, but intelligent preparation can allow it to work with any sufficiently large organism. (It probably only works with vertebrates, and two organisms of vastly different sizes are going to have trouble making this work, although if you're crazy enough to use the Crucible with them, you're probably crazy enough to develop an appropriately engineered funnel-and-harness apparatus.)
The Daedalan Crucible samples the genetic material of anything in more-or-less direct contact, converting male sperm into a form more readily usable by a female organism. This allows impregnation by any creature remotely genetically compatible with the female, and tends to create weird hybrids of both organisms. Such creatures are, for all intents and purposes, unique as future cross-breeding might produce different results. If King Minos let Pasiphaë continue to mate with that bull, the first offspring might have been the Minotaur — a humanoid bull — whereas future hybrids may have formed centaur-like creatures, or bull-like creatures covered in human skin, or a man that runs on all fours with horn-like protuberances. The science behind the Crucible is poorly-understood, and so if combinations are predictable, nobody has yet figured out how.
In Game Terms: You've got to cross several hurdles to make it happen — like getting two creatures in the same room and mating, although some variation of artificial insemination is probably more likely — but this allows for the creation of weird animal hybrids. A woman and a bull, a pig and an elephant, an owl and a bear. The magic of the Crucible means that the birth will be easier, and the female is more likely to get pregnant (if you use a system like Pendragon that tracks pregnancy rates, she should be at least twice as fertile as normal, although feel free to increase the rate even higher; if you're more narrative, then probably assume pregnancy occurs). Such organisms are probably sterile, although some mad wizard could no doubt use the Daedalan Crucible again to create increasingly weird hybrids.
Hybrids should probably be made whole cloth by the Game Master, although if you have a method of random generation — like The Random Esoteric Creature Generator — that might be a nice touch.