There are certain weather related expressions in Spanish which require the verb hacer, so you can't substitute "estar" in any of these cases. There are expressions which use estar - Está lloviendo" being one of them. For English speakers these phrases with hacer don't translate properly, but that just tells you that you have to learn them off. Neither is there any rule that explains this, so just learn them as you go and it will become second nature to you. The lesson is a good one so hang in there.
John is right. Although "frío" can be either an adjective or a noun, it is always used with "hace" - one of those that needs memorising...
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