Depending on where you're from and what you consider cold, it gets VERY cold. The warmest you can expect is for the temperature to be 5c (41f) without wind chill at the summit. The coldest it can be is easily -15 (5f) in early and late seasons or with any type of wind at the summit.
Even if you're used to living in -5c to -15c weather, you need to ask yourself "when was the last time I was outside for 8 hours in such cold weather?".
Keep in mind that the base of Fuji is usually very hot and humid in the summer, so you'll be changing quickly between sweating and freezing and back to sweating again.
Because of these weather extremes, it's very important that you bring everything on our required equipment list.