What is the overall texture in "Simple Gifts" by Aaron Copland?

I don't mean to sound obtuse, but taking your question quite literally, I would say it is homespun.

I believe this is based on a traditional Amish song.

There are many different versions of this song. Which version do you mean? Aaron Copland used it first in his orchestral score Appalachian Spring, but then also used it in his American Songs for voice and piano which was then later orchestrated again.

Simple Gifts, was also arranged by many other composers at many different times.