[gavinlit]

It's fairly high (3770 odd metres) but not a difficult climb. More of a steep walk. About four and a half hours is the climbing time from the 5th station. Start early & you'll be up there & back on the same day no problems. You may get snow in October - it's a reasonably high peak. But at least it won't be stinking hot like the middle of summer.
Official climbing season is July to end of August so you won't have the crowds but the transport won't be as great and some of the stations/huts on the way up may not be open. Most people don't go right from the bottom but instead get transport to the highest station (5th) and walk from there. Check out the touris information centre in tokyo for climbers guidebooks and stuff. If you've got a bit of time, staying in the Hakone area and looking around for a day is also worthwhile. Last time I was there they had the winter marathon going - guys running in shorts & singlets from Tokyo to Hakone. Absolutely nuts.

edit - during climbing season the most popular thing to do is get up there the night before and climb up for the sunrise. I'd guess it would be way too cold in October to do this.