Mountain goats (Oreamnos americanus) are relatively rare in the Yukon.
They are at the northern extent of their distribution and are generally
confined to the southern portion of the Coast Mountains, and the Cassiar,
Logan, and Its mountain ranges. Scattered individual sightings are also
reported. Goats are generally associated with very rugged areas which
receive substantial precipitation and are often associated with active
glaciers. The estimated total number of goats in the Yukon is 1700
animals; more than half of the goats are protected within Kluane
National Park.
Goats are extremely difficult to count and their habits make them
very vulnerable to over hunting. Harvest in the Yukon is closely
regulated.
If your looking strictly for a goat hunt I would suggest British Columbia or Alaska.