Second this recommendation. The stables are only a few minutes outside Lisbon, the tuition is excellent, the horses beautifully trained, the location is beautiful.
There are many options available around the country so perhaps have a look at a specialist company if you wish to ride for a longer period. I have personally used both
www.unicorntrails.com and www.inthesaddle.com for excellent vacations in Portugal. British companies offer cheaper prices than American ones for the same trip.
ETA Portugal is a delightful country. The people are very friendly and welcoming, English is taught in schools as the second language. Tourism is a major industry so the tourist infrastructure is helpful. The architecture is often amazing, the towns are pleasant and walkable with plenty to see and they are full of places for coffee or a cold beer. The interior, close to the Spanish border where many of the horses are bred, is still deeply rural and significantly less wealthy than the tourist coast, but the country as a whole is thriving as part of the EU. My one slight thing is that I’m not always taken with Portuguese food: I prefer Spanish!