We all have different coops, different flocks, different management techniques, different climates, and all that so we do different things. That’s one of the challenges of this forum, you can get a lot of conflicting advice and suggestions because we are all so different. When reading them you need to try to figure out what actually applies to your unique situation. That’s not always easy.
I have a much bigger coop than you do and I almost always have younger chickens in the flock, basically continuous integration. I feed and water both inside and outside because multiple feeding and watering stations makes integration a lot easier. My situation is totally different from yours.
In winter I water with black rubber bowls. When they freeze I can bust the ice out without breaking the bowls. By setting the black bowls in the sun (when there is sun) the water says thawed in pretty low temperatures. The sun never shines inside the coop, doesn’t shine at night, and some days are cloudy. I’m retired so I can go down there a few times a day if I need to take care of the water.
I have large well-ventilated coop and I do not heat my water. I’m not concerned by how much watering inside will raise humidity. A heated waterer inside your small coop could have a significant impact on humidity, especially if it is not well-ventilated. With good ventilation you might be OK with an open heated water bowl in there. If you go with a nipple system (which is a good suggestion) and have electricity out there, get someone on here that does that tell you how they keep the water thawed. I’ve seen several different ways mentioned but have no direct experience.
My run is set up so parts usually don’t get a lot of snow and it has some wind protection. Mine can pretty much go outside every day of the year. I don’t know how your run is set up or if you even have the option of watering in the run. At your elevation in Colorado you will almost certainly have colder snowier winters than I do. I seldom get much below zero Fahrenheit.
I wish you luck in finding a solution. My situation is so different from yours that I can’t offer any real concrete help. Lots of people have solved this so hopefully you can get specific help from them.