The electricity sector has a central role in the efforts to meet climate targets. Consequently, efforts are taking place to electrify industry, heating, and transportation. The Finnish government has set the target to halve carbon dioxide traffic emissions by 2030 and achieve carbon neutrality by 2045. Due to this target, the currently small proportion of electric vehicles (EVs) in Finland could expand in a manner that is difficult to forecast but could be exponential. Amid already strained investment budgets, anticipating the alternative scenarios and impacts of such a transport electrification evolution is of high importance to distribution system operators in order to optimize network planning and enhancements during the coming 15–25 years. The novelty and contribution of this paper is in utilizing a formal scenario planning process to envision what the alternative scenarios are (i.e., possible futures) for the evolution of the electric car fleet in Finland until 2040 and how these alternative scenarios could impact distribution grids. The impact analysis is performed in terms of additional energy and additional power in order to gain an understanding of the high-level impacts and investment needs. The analysis utilizes a real distribution grid in southern Finland as a case example that enables quantification. The results indicate the electric vehicles will, depending the scenario, pose an essential additional load in terms of both energy and power and that the required investment levels and investment types will be heavily dependent on the scenario.