Does Walton have any thoughts that would reveal what kind of character he is?

This is similar to your other question,

"There, Margaret, the sun is forever visible, its broad disk just skirting the horizon and diffusing a perpetual splendour. "

Walton is a romantic. He loves the elements and is sensitive to nature's splendours.

"I desire the company of a man who could sympathize with me, whose eyes would reply to mine. You may deem me romantic, my dear sister, but I bitterly feel the want of a friend."

Walton needs a like-minded soul that he can be a sensitive man with.