It is more cost effective to do laundry during evening hours. Most electric companies charge a lower rate for electricity use during off-peak hours, which tend to be evenings and weekends. Using electricity during on-peak hours, like during the day, increases demand and therefore increases price.
It is possible to save even more money by using only cold water when washing clothes. Some washers and dryers come with timers that turn on the machine at a designated time and can be preloaded. Only washing and drying with a full load is another way to decrease usage and increase savings. Finally, using a clothesline and drying clothes outside in the sun is a simple way to save even more money on electricity.