This can be done really easily with straw puppets (practice targets)and can be done once you’re shown how to assassinate.
To perform an assassination from a horse, tap the crouch (circle) button while on the horse (you’ll stand on the horse). Then press R1 to perform the assassination.
You might need to kick your target a few times if the prompt doesn’t come up, also try walking towards another target as you have to be in the correct position to assassinate.