Sure you can cut it - you can cut it as many times it might need it this winter and while not covered in snow ;-) And no, you will not need to reapply the fertilizer. It is doing exactly what it is supposed to do, despite the warmer weather. That has only activated the nutrients and they are being absorbed with active root growth. Everything will get back to normal with colder weather.

FWIW, we mow lawns throughout the winter here with no ill affect on the late season or winter fertilizing.