Chiudo la porta per non far entrare il freddo.

In Italian entrare is an intransitive verb (“to enter”) and cannot take a direct object. To say “to let something enter,” you use the causative construction fare + infinitive. So:
• far entrare = “to let/make enter”
In your sentence, per non far entrare il freddo literally means “in order not to let the cold in.”

Yes, but you’d switch to a subjunctive clause:
• Chiudo la porta perché non entri il freddo.
• Chiudo la porta affinché non entri il freddo.
Here perché/affinché express purpose and require the subjunctive (non entri). Using per + infinitive (per non far entrare) is more concise and very common.

Italian typically uses definite articles with general or abstract nouns, including many weather terms:
• il freddo, il caldo, la pioggia
Omitting the article (non far entrare freddo) would sound unnatural.

Yes. Così (“so/like this”) is colloquial and often used in spoken Italian:
• Chiudo la porta così non entra il freddo.
It conveys the same idea but is less formal than per non far entrare.

Chiudo is the present indicative, first-person singular. In Italian, the present tense can describe:
• An action happening right now (“I’m closing the door.”)
• A habitual or general action (“I always close the door when it’s cold.”)
Context tells you whether it’s immediate or habitual.

• per + infinitive (per non far entrare): concise, straightforward, common in everyday speech and writing.
• perché/affinché + subjunctive (perché/affinché non entri): more formal or explicit about the purpose.
Both convey purpose; choose based on formality and style.