The Pony Tail Palm is a slow growing palm tree. It is a very unique palm that does best in the shade or filtered sun in the afternoon. Its slow growth makes this palm perfect to grow in containers on a shaded patio or even indoors by a sunny window. The Pony Tail Palm?Aos base can slowly grow to 15 feet wide and does not like to be over watered. It grows up to15 feet high and is hardy to 23 degrees F.