Question

We know that as temperature increases, resistance of metals also increases due to frequent collisions of free electrons, and hence current decreases. Then, at colder temperature the collisions should decrease and electrons should flow slowly through the metal. But instead, current increases with decrease in temperature. Why?

Answer 1

The question is not right. 

As temperature raises, normally, the resistivity of metals or conductors increases.  The reason is the increased internal energy of the conductor increases the vibration of atoms or ions. So, the free electrons in the conduction band collide with the other electrons and atoms on the way.  Due to  increased vibrations the probability of collisions is more.  When the electrons collide, their kinetic energy is lost, and is converted into heat.

When the temperature is reduced, the atoms reduce their vibrations.  The conduction band free electrons move freely and face least resistance.  The collisions slow down electrons.  The electric field created by the potential difference between the terminals of the battery drives the electrons because of electric force.

For semiconductors also we observe a similar phenomenon.  But for insulators at very high temperatures, we have resistance reducing.