It seems most of the mountain huts in the Dolomites close by early October. Are there any open in late October?
I only know the Val Gardena area and they close mostly end of Sept/early Oct. There is a list here.
Here are 2 websites which should give you some answers related to this questions and your other post:
http://www.suedtirol.info/it/Contatto.html http://cortina.dolomiti.org/index.cfm/guida/Uffici-informazioni/