No 7 weeks is not to young what I do is put their harness on and leave it on and let them run the house with it on when they are little it hets them used to it.
As far as going outside.. here it doesnt get cold cold. If the ground has ice on it or a frost or snow then its cold for them unless you have paw shoes and a coat on them but some dogs like the cold.. IF they want you to pick them up you know its too cold.