Nikon never published a temp range for the F and probably never formally designed and tested for temperature.
That said, I used two Nikon F's in the late 1960's while working for a large Midwest daily. Both were standard factory and always functioned in any type of cold weather. I remember standing in the middle of a half frozen trout stream taking a January shot for the Sunday front page, temp about -15F. Nor problems, shot made the front page.
But, that was then, this is now, Nikon F's are decades older, lube's are gone, aged or have been changed, who knows what is used in a CLA these days.
Try it but if you MUST have the camera function, then a knowledgable individual doing a CLA is required for cold temps.-Dick