Right answer: hará
In this case, the Spanish verb hacer refers to weather conditions or atmospheric temperature.
In this way the verb hacer in its many conjugations works as an impersonal verb, that is, it is conjugated in the third person in singular, without any reference to the subject.
This means it is not necesary the subject in a sentence with these conditions.
In addition, at the beginning of the conversation, Eric uses the word mañana (tomorrow), that means we have to conjugate the verb hacer in future tense as hará.
According to this rule, the correct option is
Hará mucho frío
It will be very cold
