Beautiful coop! I agree that it needs more ventilation though. Ventilation is more important than insulation (and if you have as much ventilation as they need, it will more or less negate the effect of the insulation and even out the temperature inside vs. outside, which is fine because they need to be dry and out of the elements, not warm - they keep themselves warm with their insulating down coats). So cut a lot more ventilation out at the top, and protect it from blowing snow with awnings or something along those lines. That's what I ended up doing - check out my thread:
https://www.backyardchickens.com/threads/vent-protection-from-blowing-snow.1507449/#post-25288221
I'm a big fan of wind breaks in the run myself, because I live in one of the windiest cities of the country and winds can be brutal here, especially in the winter, and especially when coupled with precipitation. Wind is more dangerous to chickens than temperature, because they rely on the force field of their insulating feathers to stay warm, and they only work if they can maintain an unbroken surface that keeps the insulating air trapped underneath to keep them warm. Wind hard enough to ruffle their feathers break this bubble and lets the warm air out of their fluff, negating the insulating effect of the feathers, so the chickens can't keep themselves warm and may refuse to go out in the run. If given the chance, they always prefer to be outside than inside, but if the conditions outside are bad enough, they'll be forced to stay in, which is not ideal (more pooping in a smaller space makes the coop dirtier, not having a lot of room to move around leads to bullying and behavioral issues, etc.) So I would suggest giving them wind breaks so they can spend more time outside even in bad weather. What I've done in my run is two of the sides are permanently covered by faux ivy (to hide ugly stuff on the other side, and to provide a nicer backdrop for pictures
but it doubles as a wind break as well), and then the other two sides I cover up with clear polycarbonate panels in the winter. You can use clear shower curtains or painter's plastic, but I find those to be annoying to put up and take down, they rip easily, they flap too much in the wind even if tied down well, and are overall a pain in the butt. But they do work if you can't afford the solid panels. If you can, they are awesome though! They let you see in and let the chickens see out, they let light in, they don't flap or bang in the wind, and they stop both the wind and the precipitation from blowing across over the chickens directly. Even on really windy, nasty days, it feels really nice and quiet in the run - I like to sit in there with the chickens, and the panels give it a bit of a greenhouse effect, too, which is nice on those cold days. The chickens are out and about on days where they would be staying in if it weren't for the panels! The top of my run isn't covered everywhere, so they still get plenty of ventilation (so don't seal it completely), but they have enough of a protected area where they can hang out in the winter (and winter here is more than half the year).
As for water, no, they don't need water 24/7. Unlike people, animals in nature don't have access to water 24/7, unless they happen to live in or immediately next to a body of water. They'll know of a water source and go there to drink, then go back to their day. Domesticated animals are privileged to always have water at the ready, but they don't need it literally 24/7, especially at night when they sleep. Chickens don't eat or drink at night anyway, they can't see in the dark and just hang out on their roost until daybreak. You can consider adding water to the coop if you don't have an automatic door, or if you let them out manually but can't get to them in the morning, and they'll be stuck in the coop for an extended period of time. You can teach them to use a nipple waterer - that will prevent spillage or evaporation that can contribute to frostbite. Or if you don't have wind breaks or a cover over your run, and you get a lot of wind or snowstorms, they may not want to go outside, so in that case they'll need water inside. With my setup, the chickens are outside almost always, so I don't have water in the coop. I have an auto door so they can go outside early and drink, without waiting for me. The only time I bring water into the coop, is if we're having a particularly brutal snowstorm that's blowing snow into their run from the uncovered overhead section, and I can't keep up with shoveling. That's only happened a handful of times. When that happens, I bring one of my heated dog bowls into the coop, raised on a cinder block, and when the storm passes and I clear the run, the chickens go back outside and I take the indoor bowl away. It only stays in there temporarily, and I haven't had problems with it.
https://www.backyardchickens.com/threads/vent-protection-from-blowing-snow.1507449/#post-25288221
I'm a big fan of wind breaks in the run myself, because I live in one of the windiest cities of the country and winds can be brutal here, especially in the winter, and especially when coupled with precipitation. Wind is more dangerous to chickens than temperature, because they rely on the force field of their insulating feathers to stay warm, and they only work if they can maintain an unbroken surface that keeps the insulating air trapped underneath to keep them warm. Wind hard enough to ruffle their feathers break this bubble and lets the warm air out of their fluff, negating the insulating effect of the feathers, so the chickens can't keep themselves warm and may refuse to go out in the run. If given the chance, they always prefer to be outside than inside, but if the conditions outside are bad enough, they'll be forced to stay in, which is not ideal (more pooping in a smaller space makes the coop dirtier, not having a lot of room to move around leads to bullying and behavioral issues, etc.) So I would suggest giving them wind breaks so they can spend more time outside even in bad weather. What I've done in my run is two of the sides are permanently covered by faux ivy (to hide ugly stuff on the other side, and to provide a nicer backdrop for pictures

As for water, no, they don't need water 24/7. Unlike people, animals in nature don't have access to water 24/7, unless they happen to live in or immediately next to a body of water. They'll know of a water source and go there to drink, then go back to their day. Domesticated animals are privileged to always have water at the ready, but they don't need it literally 24/7, especially at night when they sleep. Chickens don't eat or drink at night anyway, they can't see in the dark and just hang out on their roost until daybreak. You can consider adding water to the coop if you don't have an automatic door, or if you let them out manually but can't get to them in the morning, and they'll be stuck in the coop for an extended period of time. You can teach them to use a nipple waterer - that will prevent spillage or evaporation that can contribute to frostbite. Or if you don't have wind breaks or a cover over your run, and you get a lot of wind or snowstorms, they may not want to go outside, so in that case they'll need water inside. With my setup, the chickens are outside almost always, so I don't have water in the coop. I have an auto door so they can go outside early and drink, without waiting for me. The only time I bring water into the coop, is if we're having a particularly brutal snowstorm that's blowing snow into their run from the uncovered overhead section, and I can't keep up with shoveling. That's only happened a handful of times. When that happens, I bring one of my heated dog bowls into the coop, raised on a cinder block, and when the storm passes and I clear the run, the chickens go back outside and I take the indoor bowl away. It only stays in there temporarily, and I haven't had problems with it.