I realize it will be cold. Would the NF be in shape. Is there much snow this time of year.

Thanks

The NF is usually in pretty good condition in October. Don't expect any snow unless there has happened to be an early storm that blows through, but do expect concrete like ice on the face, and plenty of world class scree on the approach.
The NF is a little more difficult in the late fall than in the spring, but a highly enjoyable climb. It has been soloed and roped climbed in these conditions, but you need to be very competent on 50 deg bare ice for 5-6 pitches. There may also be some mixed climbing to exit the gullies to get to the summit, depending on which route you end up on to get to the top.
If you go roped, it is definitely screws the whole way--no snow gear needed.
Any other route on the mountain should be rock and scrambling.
The weather tends to be beautiful this time of year, pretty dry and few storms. Temps are generally pretty manageable (below freezing at night , but above 0, 30-50+ during the day) with nice sunny days--but that is subject to change in a couple of hours.