What an exciting search this old photograph has led me into!
I found a reference in a writing that my Mother put together back in the mid-60's that outlined my family's history. My original picture was likely taken in 1925 or 1926 in or near Sunrise, Wyoming, where my Father was the superintendent of schools and my Mother was a high school student. (Yes, a type of relationship that would end you up in jail today, but it was handled with great care by my mother and her father, and my Mom and Dad were married in 1927, a year after she graduated from high school.)
The car is a "Dort Roadster", probably 1921 or 1922.

This is the only image that I have found that shares the characteristics of the one in my old picture of my Dad.
I did find a photo of a 1923:

You can see the major difference: the wheels. Wooden spokes on the 1921 and what appear to be steel wheels in the 1923 photo.
Here is another picture, of a 1923 Gray Dort, that shows the very distinctive shape of the edge of the fenders, easily seen in my original photo.
Here is a picture of a 1921 Dort phaeton (what would you call that body style? In a Model A, it is a Phaeton.) You can see the basic "sameness" to the roadster in my original photo: the shape of the fenders, the continuous beltline at the top edge of the doors, etc.
What a wonderful exercise that old photo has led my upon!
Thanks for all of the input from you.