Whelan and I had been chatting a goat hunt, it is indeed probably the most physical hunt in North America. Where the sheep stop, goats keep going. This said, they are not nearly as wary as sheep, if you spook sheep they'll top the ridge they're on and potentially the next one. Goats will climb to the nearest face, stand on top of it and look back. They know they live on the most ridiculous terrain there is and can climb the worst of it, to a degree it boggles the mind. Look up the Rocky Mountain Goat Foundation for a great series of videos and pics, hunting and otherwise, of mountain goats.
Interesting side fact is they're not actually a goat. They are their own genus, Oreamnos, within Caprinae (subfamily of Bovidae), and are for a shorthand forum synopsis as closely related to the goats as they are to sheep. They are the last surviving member of Oreamnos, the others having died out ages ago. Hunts are physically challenging but not impossible, you're fit enough by good measure and after one you'll probably call it good on the species. I have a fourth time mountain goat hunter coming this fall and I'll analyze him to determine why.
Weather can be atrocious given it's the mountains in fall. August weather is generally the best, but the goats can be high, they like to stay cool and food is still plentiful meaning they don't have to huddle near it. Hair will be shorter in August, many consider this to be a big part of the trophy, I personally think the experience is the trophy. Now the disclaimer is these comments come from an early thirty-something that mountain treks for recreation, I had to helicopter out one client last year on a mountain goat hunt who lost the ability to walk.
It's an awkward ground for me to describe and as such you'll see me describe goats variously as the hardest hunt we have and totally doable. I also think bang for your buck, in scenery, experience, and effort it is the best value trophy North America has. You'll spend at least double, and more likely triple goat hunt's price to hunt sheep, and you could easily spend a half dozen goat hunt's worth to hunt a stone sheep which are running all over the mountains ranges to the north. I'm cooking dinner and about to be slaughtered when my wife gets home for the lack of progress, so forgive typos and I'll get back to this thread.
