According to the Handbook of Texas, a family named Winder was so large that it doubled the population of Morton.

Since Cochran County was one of the last in the state to be broken out into farmland and settled, the motto for Morton became "The Last Frontier".

Morton was spared the fate of many Texas towns that shriveled and died after being bypassed by the railroad during the 1930s and 1940s.

The topography of the area is generally flat, with higher elevation to the western part of the county, gently sloping downward to the east.

The center of the city of Morton (location of the county courthouse) lies adjacent to the northwest corner of the intersection of State Highways 114 and 214.

About 20 miles (32 km) to the north of Morton, along Texas State Highway 214 is the Muleshoe National Wildlife Refuge, home to a large sandhill crane migration each autumn, and year-round home to a sizable prairie dog town.

Winter days in Morton are typically sunny and relatively mild in the mid-50s °F, but nights are cold, with temperatures dipping to the mid-20s °F.

As of the 2020 United States census, there were 1,690 people, 700 households, and 467 families residing in the city.

The Morton Memorial Cemetery is about 2 miles (3 km) north of the city center on Highway 214, and is a maintained final resting place for former members of the community.

Remains of some Native Americans are also buried there, with a large marker, on the western end of the cemetery.