Energy consumption in buildings plays a significant role in the global energy demand. The European Union has promoted different regulatory directives in the framework of energy efficiency to develop the construction of buildings with nearly zero energy consumption. The main objective of this paper is to simulate how the design characteristics of different factors of the window elements of buildings (frame, glass, and shading systems) located in a hot climate region affect their cooling primary energy consumption. For this purpose, a comparative analysis is carried out with multiple simulations of different types of single-family residential dwellings using the EnergyPlus energy model. From the results obtained, it can be deduced that, compared to the standard design configuration, the primary energy consumption for cooling of the buildings studied can be reduced by up to 12.7% and 29.5% by modifying the design characteristics of the frame–glass assembly or the shading system of the window openings, respectively. The conclusions drawn from this study can serve as a reference in normative and regulatory documents affecting the building sector for the establishment of minimum requirements for certain characteristics of the constructive design of buildings.