It will be mostly mild, with some chilly nights. There will be some rain on the 6th and 7th of October and on the 24th a heavy thunderstorm.. otherwise dry until the 2nd of November when it will rain continuously for 11 days..
But generally, autumn in Northern Spain is mild and pleasant in the daytime but can get quite chilly at night. I was lucky to walk for 10 days with no rain last November, but I've been soaked through on previous caminos in September so who knows? But be prepared, bring layers and a poncho or rain jacket and you'll be fine whatever it throws at you..