John - There’s a good chance that you won’t run into winter conditions on the JMT in October. On my last JMT hike I finished on Whitney on October 9th & had balmy (60’s) daytime conditions & cool nighttime temps (20’s). Other than the high passes and Whitney, the JMT was snow free, bug free, and Ranger free - a great combination. I only ran into 3 other hikers (2 PCT & 1 JMT thrus).
The only challenging situation that I faced was on the multiple switchbacks coming off Whitney on the East (Whitney Portal) side - they were covered in thick ice & I wished that I had my ice-axe. Obviously I survived 
I ran into an old-timer in the Yosemite backcountry who mentioned that during his lifetime (he was in his 70’s) he never saw a major snowstorm in the High Sierra before mid October & often the first major dump occurred in November.
As far as resupplying, I resupplied in Tuolumne & at VVR (Vermillion Valley Resort). In October of '05, VVR’s hiker ‘box’ (its actually a 55 gallon drum) was FULL of extra hiker food from the summer - I was eating mostly freeze dried food that I would never normally buy until I finished the trail. If you plan on going to VVR, make sure to check ahead on their closing date. (BTW if it weren’t for the hiker box, that resupply would have cost a small fortune - the VVR store is pricey)
Happy Trails,
freebird
freebird