For horse riding near Addis, you can give Lance a call on 09 11 82 58 82. His place is in the countryside just 20 kms from the capital near the small town of Menagesha on the Ambo road. You can also find Lance at the Garden Paradise restaurant that he owns, near Old Airport/Vatican.
Another place to go riding in the capital is Beka Ferda, which is even closer to Addis, in the hills above the city.
For treks in Bale, you can get in touch with Mark Chapman from Tesfa Tours . Mark is also a stalwart of the Addis Ababa polo club – so he knows everybody in town with an interest in horses.
Marc can organise the trek for you, and also has good saddles and camping equipment. You can organise it yourself – but that will mean using local saddles.
Another place is the horse riding in Lephis, near Langano. Again, you can organise this independently, but I suggest going through Mark.