The town's unusual name is taken from part of two neighboring cities, Guin and Winfield. "Gu-Win" and "Guin" are not the same, though the pronunciation is virtually the same, leading to occasional confusion by visitors.
The town does have a City Hall building and until the early 1990's had a police department consisting of a single officer and police car. The building is currently vacant.
There were 86 households out of which 31.4% had children under the age of 18 living with them, 62.8% were married couples living together, 8.1% had a female householder with no husband present, and 25.6% were non-families. 25.6% of all households were made up of individuals and 14.0% had someone living alone who was 65 years of age or older. The average household size was 2.37 and the average family size was 2.81.
In the town the population was spread out with 20.1% under the age of 18, 10.3% from 18 to 24, 29.9% from 25 to 44, 20.1% from 45 to 64, and 19.6% who were 65 years of age or older. The median age was 38 years. For every 100 females there were 108.2 males. For every 100 females age 18 and over, there were 94.0 males.
The median income for a household in the town was $29,375, and the median income for a family was $42,500. Males had a median income of $39,375 versus $18,906 for females. The per capita income for the town was $16,868. About 11.3% of families and 9.9% of the population were below the poverty line, including 5.3% of those under the age of eighteen and 6.8% of those sixty five or over.