They're at the corner of E. Yandell and Willow in south El Paso, just north of Interstate 10 and not far from the U.S.-Mexico border.
The shop is sort of an industrial-looking place and I don't know if they have a real retail store (they don't mention one or any hours it might be open). I believe most of their stuff is special-order, so I don't know if they have any off-the-shelf merchandise. Here's their address and phone, give them a call:
El Paso Saddlery
2025 E. Yandell
El Paso, Texas 79903
Phone: 915-544-2233