I have open coops and the only lamp i use is enough to be able to see. They huddle together and mill around like any other time…they can be incredibly hot…..i would use a flat or wider footboard to roost so their feet are covered by their down otherwise they will get frostbite….. Chickens need wind and weather protection coops are nice where they can decide but if they are protected from the cold tooooo much then they will not be weather / cold hardy. I have more health problems this time of the year when the weather gets day hot & humid and nights start to plunge into very cold.Welcome! And yes this is a very good place to ask all your questions.It's great that you're thinking ahead so you won't be caught unprepared!
If this is your first winter in Washington, are you quoting historical info. for you neighborhood? Your ID says you're in Seattle so it's a little confusing. BUT......
Please be very careful about covering your coop entirely with anything. Even in the winter they need PLENTY of ventilation. LOTS. Without plenty of ventilation humidity and ammonia will build up inside the coop and cause respiratory sicknesses. It's best to avoid drafts blowing through on the floor or directly on the birds, so it's good to put screened vents near the top, under the eaves.
If you have sturdy breeds (RIRs are one example) they are incredibly hardy and will withstand just about anything Western Wash. can throw at them if they are in a dry, well ventilated, non-drafty coop. Breeds with very large combs are generally better suited for warm climates; their combs are more susceptible to frostbite. Breeds with smaller combs are less vulnerable. Chickens' feathers provide a lot more insulation than most people realize. Think of all the birds we see flying around in the winter. They don't even have a coop and survive very well. Keeping their coop cozy warm during the night and then sending them into the fresh cold air during the day isn't doing them any favors. But, if you feel you must use a heat lamp so that YOU will sleep better at night, be ABSOLUTELY sure you get a fixture with a CERAMIC fitting that is rated for the extreme wattage of a heat lamp. MANY birds are lost each year because of fires started by improper wiring and undersized light fixtures.
Whichever route you take, have a great time watching your birds in their first snow. It's lots of fun.