Is the mountain you are talking about mount eagle pass?

If I wanted to be safe I would slow down to 35mph at the start of the down hill and use 1st gear. If the speed climbs above say 45mph, I would give the brakes a stab to slow down and then get off of them again.

Extra brakes on trailer? A good idea.

All of this assumes that you have a brake problem in the first place. Since you don't know, be extra cautious the first time and work your way up.