Do a section of the High Sierra Loop, if you can get permits. I did a 3 night, 4 day trip in August. (Perhaps I'll actually sit down and do a trip report w/pictures soon) Staring from Cathedral Lakes TH to Sunrise HSC, (~8 miles) to Merced Lake HSC a long detour to Clouds Rest (~17 miles), to Vogelsand HSC (~8 Miles), back to my car (~9 miles). You hit some chunks of the JMT along the way.
You can cut the 2nd day to 10 miles if you don't detour to Clouds Rest, and hit a nice chunk of the JMT.
Most people I met were going the opposite direction as me, because Merced to Vogelsang is a 3200' elevation gain, vs 2200' feet Merced to Sunrise.
There's what, 6 HSC, all 8-10 miles apart, so you can put together some nice loops or partial loops if the shuttle is still running in Tuolumne, depending on the kind of terrain you want to see.
There shouldn't be any accumulated snow in October, but snow certainly could fall,(and melt) You'll want to read the weather forecast, but all you'll need is more warm gear than in the summer. A heavier down jacket, a 20 degree sleeping bag, decent ground insulation, hat, gloves, etc. The only place you wouldn't be able to have a fire is Vogelsang, and I had no trouble finding down and dead at the other two as long as I was willing to walk a little.
If you're cooking with a cannister stove, read up on this website on how to make sure it works below freezing, as that can be a issue.
If you are really concerned about weather, just plan your trip so that you're never farther than a short day's hike from a TH, so you can bail if you have to.
Desolation Wilderness also goes off permit on Oct 1, I believe, and there's plenty of great shuttle hikes,or short loops there as well.