If you want to spend a half day horseback riding in Buenos Aires, I can HIGHLY recommend
http://www.caballos-alapar.com/ Caballos A La Par
My wife and I did this just the other day, and Adrian (owner) was simply an outstanding guide and instructor. I've only been on a horse 3-4 times, my wife is a bit more advanced, but Adrian got me walking, trotting and even short galloping during our tour through one of the national parks where his ranch is located. (its about 35 minutes outside of buenos aires, and they provide transportation to and from).
Absolutely beautiful scenery in the park, you go through forest areas and cleared pastures, we had a great time and I highly recommend it whether you're an advanced rider or never been on a horse before. And he treats his horses like family, they are so well behaved and maintained its unbelievable.
Adrian speaks good english as does his assistant Miriam who is from Holland I believe and was our driver to/from the ranch (but she also comes out on some tours).
Let me also add that if you want to do this activity you should book in advance as much as possible as he fills up quickly... while we were there he got a number of calls for people trying to do same or next day reservations and had to decline them all.