Well, I can give you some opposing viewpoints, lol. I don't care for external nest boxes for several reasons. They are fussy to build and weatherproof; it is easy to get a leaky one, and yes, they would be a little colder than the inside of the coop, I would think. Once built, you can't easily modify them. I am going to walk into the coop every time, anyway, to check on things in general and to look for eggs laid outside the nests. Nests inside the coop can be made of anything from a cardboard box or 5 gallon bucket to an elaborate rollout design. Even a pile of hay in a corner makes a good nest. They can be moved and modified. Another type can be added, such as changing from front to top opening, to try to encourage a hen to use the nest boxes. Even if I had a small, reach in coop, I would use something like a plastic dishpan, for ease of cleaning, if nothing else.
Plenty of people have them and like them, I realize. I'll have to let others tell you the pros!
Good luck, whatever you choose to do!
