<p>I am working with Ender 3 Pro and in menu it has an option to cooldown. Is there any need to cooldown 3D printer before shutdown or can I just shutdown without cooldown? </p>

Depending on what material you print it it most likely a good idea to let the hotend cool down before shutting off the printer (fan).
For example if you shut down the printer right after you print a PLA part, at 190 - 220 degrees Celsius, your hot end will still be that hot and will suffer heat creep without the fan running. The next time you fire up your printer the hotend will be jammed and you will need to clear it before starting a print.
This is obviously situation dependent but in most cases you should let your hot end get below the TG (glass transition temperature) of the material before turning off the printer.