In reply to galpinos:
All the main Dolomite areas are great for walking, but if I was choosing it would be the Pale di San Martino or the Brenta groups, because they offer the chance to get into some really wild areas. End of October can be absolutely idyllic for walking and even climbing in The Dols, but it can also be distinctly wintery, and you would need to be careful not to get snowed into some remove bivouac hut.
The long term weather outlook is for good weather right through October but with a changeover around the end of the month.
If you found that things had gone distincly white, then you have plenty of pre-Alpine walking to do where I live, or further down around Lake Garda.
Thinking about it more, I would go walking on the (very easy) glaciers of the Adamello group (just west of the Brenta Dolomites) because a bit of fresh snow basically makes no difference to your plans. Gorgeous free bivvy huts up there, and almost nobody around at that time of year (not even me, I have work in Tuscany all of October).