Executive dysfunction (ED) is a characteristic of Huntington disease (HD), but its severity and progression is less understood in the prodromal phase, e.g., before gross motor abnormalities. We examined planning and problem-solving abilities using the Towers Task in HD mutation-positive individuals without motor symptoms (n = 781) and controls (n = 212). Participants with greater disease progression (determined using mutation size and current age) performed more slowly and with less accuracy on the Towers Task. Performance accuracy was negatively related to striatal volume while both accuracy and working memory were negatively related to frontal white matter volume. Disease progression at baseline was not associated with longitudinal performance over 4 years. Whereas the baseline findings indicate that ED becomes more prevalent with greater disease progression in prodromal HD and can be quantified using the Towers task, the absence of notable longitudinal findings indicates that the Towers Task exhibits limited sensitivity to cognitive decline in this population.