Hello, I am also moving to Harlingen in June. I grew up in the area and my Husband and I are moving back. I have been looking for places for my horse as well. If you don't mind the commute, there is Farasi Farm in Los Fresnos, TX. Their website is
http://www.farasifarm.com/blog.html I have my horse at this farm at the moment. In Harlingen itself, I found Classic Farm and Stable while driving around, but upon talking to the owner, she's retiring in a few months. Her clients are in the process of finding other stables. She gave me the website for the local Arab association to look for a place to board.
www.rgvahc.com I will let you know if I learn anything else. Please, if you find a place you like, let me know too.
Thanks
Ellen