There are two answers to your question. I live on the coast and get 80" of rain per year here, it rarely freezes and the summers are not hot.
1) By "Breed" you are limiting yourself a bit. Crossbreeds/hybrids are the best layers.
2) I raise the following:
Layers/Breeders: Barred Rocks, RIR, Jersey Giants, Marans, Black Sex Links, Red Sex Links, Speckled Sussex, Dark Cornish
Meat Chickens: Freedom Rangers
All those layers are tolerant of our climte. I would say the best all around 'breeds' are the Barred Rocks, Black Sex Links and RIR's.
I would say the Speckled Sussex, Cornish and RSL's are the prettiest.
So if you are not raising eggs for sale, pick the birds you can most tolerate looking at because you'll be seeing them every day to collect eggs, water and feed. I really can't think of any of the large breeds that won't work in our climate.