In the Alps there is a dense network of huts mostly maintained by the local alpine clubs. There are also some private huts mostly owned by mountain guide associations.
Most of the huts are closing down towards the end of September but many have winter rooms or small bivy huts that are accessible for the whole year. Especially Italy has a lot of bivy huts that are not managed at all.
Check maps of the region or websites of the alpine clubs for huts.
Regarding the car... You likely won't need a 4WD. Valleys in the Alps have quite good infrastructure and the gravel roads after the last village are usually closed for public traffic.
The gear required strongly depends on the weather, the altitude and the exposition. A North facing hiking trail in 2500 to 3000 meters may already be snowy or icy in late October. But this really depends on the weather and is really hard to predict. South facing routes should not be problematic.