Vail Residence Inn is open according to their web site. I guess they won't be doing much business until ski season.
No mention of shuttle to the slopes (yet) anywhere on there web pages. I can't imagine them not having a shuttle. But then again there are no pictures of their rooms yet either; however, there are room descriptions and all come with full kitchens, but only the 2 bedroom units also have an oven.
With its location just up N Frontage Rd from West Vail Mall, and with sidewalk access 0.4 miles down to City Market and 0.5 miles down to Safeway, that along with a shuttle to the slopes would be very convenient and mean no need for a car as that would save $45/night hotel parking and up to $40/day for town of Vail parking. FWIW, there is Buffehr Creek bus stop eastbound (to the slopes) 0.2 miles from the hotel on Chamonix Ln, half of that walk is slightly up hill and has no sidewalk and walking there could be a challenge in ski boots and with skis and poles (easier for snowboarders IMO). Returning to the hotel the westbound bus stop is much closer (400' away right on the N Frontage Rd), relatively flat and sidewalk all the way. Alternatively, I guess one could also pay for ski storage at the slopes, or if renting skis/snowboards store them at Vail Sports, Vail Ski Tech or from whomever else they're rented.