We've done all those roads with a 2014 gas coach towing large toads. There doesn't have to be any drama. Just pace yourself uphill and watch your temperatures. Make sure your cooling system has been well maintained.
Proceed downgrade in a similar fashion, use whatever gear works to allow the engine to hold speed with only intermittent brake use. It's not a race. Never apply and hold the brakes, use them intermittently so they cool between uses.
You shouldn't need to stop and cool anything off, cooling works better in motion with airflow.