During my time on Merseyrail, the traction power at night was off only for engineering possessions, including the nightly underground maintenance possession, track & melamine panel cleaning and other operating requirements.
Because of the location of electric sub-stations, the nightly isolations covering the underground also affected some overground locations.
During Winter, De-icing trains ran as required and 507/508 units not inside sheds were left switched in. In extreme cold they were sometimes moved few feet to ensure they would be serviceable in the morning. The 503 units were better protected from frost and started without difficulty at below 20F.
One advantage of the traction current being on at night, is that when circuit breakers operate for whatever reason, staff are quickly made aware and can respond.