Dont let him sleep outside. Even if you have to put him in after dark when the hens are roosted. They wont pick on him after dark.
Sorry Kinda long
A couple things you can do
You can get a small matt heater that is for dog houses or cat beds. Get the outdoor waterproof one. They are safe in a coop and they add just a bit of warmth not too much just enough to help keep your coop dry and keep the chill offI have a small coop that is 4'x4' x 4' high. My coop walls are about 3" thick and insulated with some reclaimed drop ceiling tiles between plywood they are old fiberglass type. I would not call it great insulation like in a house but it helps.
When I had just two chickens I used a light bulb and changed the wattage according to the temps outside. My coop was too small for the usual 250 watt bruder bulb because I could not get it high enough off the roost area to keep them from getting burned. (has to be 18+" from tallest chicken head to be safe) I started out with a 40 watt bulb for cool nights like 25 degrees, then if it was going to be below zero I used a 65-75 watt bulb. I had about 10" of clearance but put it towards one end and they would not sit under it just next to it. This was enough for two chickens..
I now have 8 chickens and they can keep warm together. they fill the roost perch, but I wanted to make sure they did not have trouble staying warm in snow storms and below zero days/nights.
I have a heated outdoor dog house type matt that is about 20x15 or so. This heats the coop enough to keep moisture out and take the chill off.
You might take a look at what is in the coop as far as bedding.
Are you using sawdust, straw or hay.
My experience has told me..... Put sawdust on the floor then cover with straw, or hay. This year I have used hay and it will hold moisture but if you air out the coop during the day and you replace it once a week it helps. Straw absorbs some moisture and has great insulating properties, but from what I can see the hay is helping eliminate moisture because its drawing it to the sawdust. Straw will not draw moisture out.
I
t all is quite technical believe it or not and you have to experiment and observe. And it can change from year to year depending on weather and humidity ect.
The key to some things like this is proper ventilation as someone mentioned.
Let me explain how mine works
The small opening in the coop they enter through has a locking screen door for at night to keep predators out. I put straw or hay up against that door at night from the inside. This allows air to pass in and push the warm air up. Often times there is frost on the top of the opening in the morining this is the moisture that is escaping from my coop.
The straw and hay allows air to flow but not a draft. Creating a dead air pocket so it gets warmed to some degree by the heater that is on the floor.
My first year with two chickens I had moisture with the light and often I would put the solid door on at night. That was the wrong plan.
After I had 6 chickens I had moisture issues on the nights I blocked the door off. I now have 8 chickens and dont block the door and have no moisture building up in the coop. I did have frost on the window at -10. But they roost right in front of that window so I am sure that it is persperation.
I also wrap the pen with tarps for winter to keep the wind and snow out.
As I said the key is experiment and observe. you will learn what to do for your situation. The vasaline will not fix the frost bite he already has but it will keep him from getting more.
Good luck