Pendulum clocks generally go fast in winter and slow in summer why

The relation between Time period and length is $T\propto \sqrt{\mathrm{l}}$

In summer, due to increase in temperature, length of pendulum increases, time period also
increases and clock losses time, hence it goes slowly in summer.

In winter, due to decrease in temperature, length of pendulum decreases, time period also
decreases and clock gains time. Hence it goes fast in winter.