I don't know how many chickens you plan to have, but as long as the chickens have room to get under them, they don’t take available space away from them as far as room in the coop. It sounds like you will have a walk-in coop so you should have plenty of height to use. They can take away room for roosts, feed, and water though so that’s something to consider. You could build them under the roosts and use the tops as a droppings board. No wasted space there. Or build the coop a little bigger. You might follow the link in my signature to get my thoughts on space. In your winter climate, unless you have a run that will stay at least partially snow-free, you want to err on the side of making the coop too big.
If you wish you can still make a door to gather the eggs from the outside, just hinge it to swing sideways, down, or up, whichever you prefer, but I like going inside the coop regularly. I’ve found a dead chicken, an injured chicken, snakes, and even a possum by going inside that I would have missed if I had gathered eggs from the outside.
If you do hang them on the outside, you can always insulate them to cut down on them losing heat. It won’t add any heat but it will slow how fast they cool off. Chickens will eat certain types of insulation so you need to cover it so they can’t get to the insulation. Even inside the coop it’s possible you could get frozen eggs on your worst days of the year, but gather them as often as your schedule allows to avoid that.