Hmm... terreno is more colloquially used to mean property as in "this is all part of my property" = "isso e' tudo parte do meu terreno."
You said: "isso tudo é parte da minha propriedade/das minhas terras"; terreno is a definite area of ground, urban or rural...
"The terrain on which the hospital was built is my property" / "o terreno no qual o hospital foi construído é de minha propriedade"
I should have stated that better. When the word is used colloquially, it has a broader meaning. Many Brazilians use it to mean their land of ownership. "Depois dessa marca começa o terreno do meu vizinho." You would never say the same in English. "My terrain ends at the end of the grass" would never fly. Terrain has a more focused meaning, imo. Cheers.