A nuclear war is a war in which nuclear weapons are used.
MAD
M.A.D. meaning mutually assured destruction represents a scenario where a small nuclear attack by one side would cause repercussions so great that both attacker and defender would be destroyed, along with much of the rest of the planet. The Slitheen family attempted to create such a scenario on Earth by attacking the rest of the world with Britain's nuclear missiles, thereby reducing the earth to molten slag. (DW: Aliens of London / World War Three) Blon Fel-Fotch Passameer-Day Slitheen again tried to use nuclear technology to her advantage in Cardiff. (DW: Boom Town)
Other M.A.D. scenarios took place on the planet Minyos rendering it uninhabitable, this was indirectly caused by the Time Lords.
The effects of nuclear war
During the one thousand year war on Skaro many were injured due to the use of nuclear, biological and chemical agents. Davros discovered the final form they would take through the mutation and created a life support system, thus creating the Dalek race.
Also on the planet Argolis a war lasting just 20 minutes caused so much damage that the planet's surface became uninhabitable and the Argolins became sterile.