Supposedly the Durango area ski resort, Purgatory, is the closest Colorado ski area to Texas.
This picture is from Purgatory Flats, a trail accessed immediately across from the ski area. The mountain is 'Engineer', a great late summer high altitude Colorado scramble. Though not Whistler, the ski area has an active summer program, including water slides, etc. A chairlift ride to the top is $3.00. I've no idea if pets or mountain bikes are allowed.