Teddy was a man's man. A conservationist, big game hunter, and yes, a conservative. He had soem "progressisve" ideas, but the word progressive back then did NOT mean left wing. He was a FRIM believer in American exceptionalism. In fact, he embodied it, to a large degree.
Was he a man's man?
Definitely-- Teddy was that and more, he was an exceptional painter, poet, historian, one could go on and on.
He was, as you say, an exceptional man who believed in the exceptionalism of America...
But he was NOT a conservative.
He believed in American exceptionalism, yes, but not in the wisdom of the Founders, or in the free market.
His conservationism, while moderate and wise compared to the enviro-whacos of today, was also largely misguided, NOT because Roosevelt did not know hopw to conserve nature-- he did-- but because in grabbing land for the government to control, he assumed such wilderness areas would be managed in the future by men who knew as much about them as he did, a hope that was to be disappointed in his own lifetime: http://184.108.40.206/focus/f-news/1551707/posts
TR famously urged
"far more active governmental interference with social and economic conditions in this country"
Those aren't the words of a conservative.