Smart grid solutions with enabling technologies such as energy management systems (EMSs) and smart meters promote the vision of smart households, which also allows for active demand side in the residential sector. These technologies enable the control of residential consumption, local small-scale generation, and energy storage systems to respond to time-varying prices. However, shifting loads simultaneously to lower price periods is likely to put extra stress on distribution system assets such as distribution transformers. Especially, additional new types of loads/appliances such as electric vehicles (EVs) can introduce even more burden on the operation of these assets, which is an issue that needs special attention. Such extra stress can cause accelerated aging of distribution system assets and significantly affect the reliability of the system. In this paper, the impact of a smart neighborhood load on distribution transformer aging is investigated. The EMS of each household is designed to respond to prices and other signals emitted by the responsive load serving entity within the relevant demand response strategy. An optimization framework based on mixed-integer linear programming is presented in order to define the EMS structure. Then, the equivalent aging of the distribution transformer is examined with a thermal model under different scenarios. The case studies that are presented indicate that the integration of EVs in residential premises may indeed cause accelerated aging of the distribution transformers, while the need to investigate the efficiency of dynamic pricing mechanisms is rendered evident.