Around here snakes are a fact of life, whether you have chickens or not. We routinely find snakes in the yard, under our raised porches, and even on the porches themselves. I've gone in my old coop to find a snake slithering along the top roost during the day. We live in 40 acres of forest with several creeks running near the house. To call us rural would be an understatement. I finished our newest coop at 10:30am and killed the first snake at 1pm that afternoon. The chickens weren't even in it yet! We moved our coop from a 1/4 mile away, to our side yard so we (me and the dogs) can better protect the flock.
Our biggest snake problem is that they eat the eggs. We collect everyday but sometimes they crawl in the coop before I get there and get them first. But our rooster tried to fight one off last year and got badly hurt. He was bitten and was blind for a month. Poor fella, my wife nursed him back to health eventually though. So my experience is that they can be a danger to any chicken, any time of day. They will kill and eat baby chicks if they can get to them. We keep our chicks in a more secure brooder until they are old enough to at least hop up on a roost to get away from the snakes.
You can see from my photos that I just have chicken wire everywhere. AArt was right that the welded hardware cloth is much better! If I could afford the 1/4" wire I would have wrapped my whole area in it. Your setup is a lot safer than mine. Not much is going to get in to an opening that small. Snakes will get in any opening they can, so even though you have a secure coop, they can still go in the open door if you free range during the day.
We have 3 Bassett Hounds, Maybelline, MathildaBelle, and Dixie (who can smell the UPS truck from 1/2 a mile away), they are the trackers; a Black Lab/Pitt Bull mix, Tink, she actually catches and kills what the others find; and a full blooded Pitt Bull male, Zeke, who just looks scary but is actually an air conditioner addict and a big baby. Unfortunately one of the bassetts, Dixie, was not a country dog when we recused her last year and decimated our flock while we were gone one day. We learned she has to be locked up if the ladies are free ranging. If you get another pup to guard your chickens, study at all the articles here on BYC about training dogs.
WARNING: graphic photo below! Don't look if you are scared
This one crawled under a broody hen last year and never woke her up. It went through the side of the milk crate, swallowed an egg and couldn't get out the other side. I had to chop him in pieces to get him out.