I too live in LA,, La crescenta to be exact...my chicks are in a 3/8 plywood coop, with vents on the top and one side open to the run.   there is also a poop screen on the bottom of the coop that is open., my point is they have a draft..  they sit on a 2x4 perch every night and get up and lay every morning,  last week when it was snowing i did cover the open side with some heavy rubber. its warm in there at night and they seem fine,,, although i do have 5 chickens, so they keep each other warm. 
i get another chicken and cover the side of the rabbit hutch. they will be fine.
last year i was in Switzerland this time of year and it was cold, wet and snowing,,, the chickens were all out checking out the snow and seemed fine,.,,
	
		
			
		
		
	
				
			i get another chicken and cover the side of the rabbit hutch. they will be fine.
last year i was in Switzerland this time of year and it was cold, wet and snowing,,, the chickens were all out checking out the snow and seemed fine,.,,
 
	 
 
		 
 
		 
			
		
		
		
	
	
			
		
 
 
		
 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		 
 
		