Yes, albeit indirectly. See below for more detail.
Equilab can track one device at any given time (for any single account). Once you finish and save a ride, you can duplicate it. To do so, select a ride and tap the three dots in the right upper corner and then select the "Duplicate" option.
You'll then have a replica of the training, which you can assign to another horse by tapping the same three dots and choosing "Edit".