Sometimes, you can get away with not needing to re-install Windows, but not always and even if you can, re-installing is recommended. You shouldn't need to actually format the drive unless you want to although again, I'd recommend it. This reduces the chances of having stability issues related to the motherboard.
Im installing a new motherboard with a different chipset and therefore I will be reinstalling windows as well, but would it be necessary for me to format the hard drive as well?
Re-Installing the os is not necessary every time when we change the Chip/Board. Just update the bios and Install all the drivers. Do a complete anti virus scan. It will work install latest drivers only. Still if there is a lag you feel. then reinstall.