I'm starting to wonder now.... in such a scenario, perhaps the EMH wouldn't need to transform into a horse in the first place, perhaps he could simply transport both of them out of there.
The EMH is in a random desert, so he must have the mobile transmitter with him. In Drone we see a Borg, created by the fusion of Borg technology and the 29th century technology of the transmitter. That Borg ('One') has internal transporter nodes. We know contemporary Borg probably don't, so that technology must have come from the transmitter (at least partly). Which might mean that the mobile emitter contains a transporter function (or at least the technology for it), they just never tapped into that potential. If this is true, then the question would be whether that internal transporter could also be used to transport another person.