I've gotten through Thunderfist Mountain at level 5, without invisibility. It did require some save-scumming to make sure that there were no Minotaur Headsmen or Lords right outside the exit from Nighon Tunnels, but I found it pretty easy to dodge the Eyes' beams, even if there are some Evil Eyes in the mix.
I HIGHLY recommend getting a tome of Town Portal from the Master Water Guild in Bracada, making sure your Wizard is of sufficient skill to learn Master Water Magic, and making him/her learn Master Water Magic from the trainer in Mount Nighon.
Why? Just out of curiosity. Is there any particular advantage to getting to Nighon that early? Or is it more for the challenge?