Is it even ok for a puppy to be outside at 7 weeks of age??
I am thinking more in the lines of vaccinations rather than weather. If a pup isn't fully vaccinated, it may not be good for them to be outside on the ground where they can pick up diseases. Pet stores or any public places would also be a no no!!
7.5 weeks old is awfully young for a pup to be away from it's mom and litter mates
12 weeks and up is the recommended age. I am sure the move to a new home, at any age is a bit traumatic though. It may take him a few days to adjust to the new house and new routine....including a potty routine.
The pee pads are a great idea!! It's really too cold for little ones to go outside in the winter. My 4 lb guy wears a snow suit to go on walks when it's 50 degrees out, so I'd imagine it's got to be freezing to a little puppy.