What will it be like in January?
No one knows. It’s weather which is often unpredictable.
You can use Google and type in “ average January weather temperatures Florence Italy “ as a start.
What "it" do you want information on? Weather? Crowds? Tourist attraction open hours? Hotel prices? After Christmas sales? The seller's markup on gold in the Ponte Vecchio stores? If the outdoors lampredotto sellers will be hard to find? All month or just selected weeks?
Colder than July.
Of that I'm 100% sure.
Let's try... Less crowded after the 6h of January? Of that I'm 60% sure.
Yes. Definitely less crowded after 6th of January.
But not because the Florentines celebrate the Jan 6 Capitol attack in Washington DC. But rather because Jan 6 is the Feast of Epiphany. That's the holiday when Italian kids receive candies (or charcoal) in their hanging stockings from the broomstick riding Befana.
To paraphrase a former US president, it depends on what the definition of 'it' is.