There are several places in Snowshoe. Don't bother with the Snowshoe Rental Program, though. They won't even think about pets. www.snowshoevacationrentals.com
is a good start. If you do a search and check the "allows pets" you will see 17 different rentals. The old Misty Mountain, now Mountain Valley Properties, http://snowshoerentals.com/
has 5 rentals, including one at Whistlepunk.
Rentals that are pet friendly are catching on. Before my "son" passed on, I had taken him to Stowe, Tremblant, and was thinking of Whistler. Snowshoe's management is still in the Middle Ages when it comes to customer service in their food and lodging, so you need to look for a non-Intrawest vendor.
Canaan Valley has several too. http://www.homeaway.com/search/refined/west-virginia/canaan-valley/region:8309/Suitability:pets+considered