Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
Yes, it is permissible for a person to say: “I caught a cold because of changes in the weather”; because changes in the weather are among the causes that Allah تعالى has made to have an effect in the occurrence of colds and common cold symptoms.
However, one must believe that Allah تعالى is the Creator and the One who determines all things, and that causes do not have an effect by themselves or independently of His will. Rather, Allah has given them an effect; if He wills, He allows their effect to take place, and if He wills, He prevents it.
The mistake is for a person to believe that a cause has an effect by itself, independently of the power of Allah. Likewise, it is also a mistake to deny the effects of causes that Allah has made causes for their corresponding effects.
The correct approach is to affirm that causes have an effect while believing that their effect occurs by the permission of Allah تعالى. For example, fire is a cause of burning, yet Allah may prevent it from having its usual effect, as happened with Ibrahim (Abraham), peace be upon him.
And Allah تعالى knows best.