The cold temperatures can put a strain on the electrical grid when people use more electricity in the winter months for electric space heaters and electric furnaces etc.
Which can cause the power to go out due to being overloaded causing a circuit breaker to trip and then need reset.
The cold weather can also cause the power lines insulation to become brittle which could crack the insulation leading to a short in the wiring.
Temperature changes can also affect how the electricity flows through an electrical circuit by changing the speed at which the electrons travel.
This is due to an increase in resistance of the circuit that results from an increase in temperature.
Although cold weather can cause power outages it's usually not due to the cold weather itself but instead it's caused by ice buildup on the power lines which causes them to sag and break or ice causing trees to break and fall on power lines snapping the power lines and power poles.