Skiing has quite a fast learning curve vs. most sports (golf and tennis for example) to reach a level that is quite enjoyable. Thus the destination resorts are full of contented intermediates who ski just one week every year. I am also living proof, as I have poor natural coordination and failed miserably at most sports as a kid.
You location is enviable as you have a reliable 6+ month season, should be able to start on easy beginner terrain at Alta or Brighton by Dec. 1 at the latest. Take a lesson as a first timer, then practice and take more as needed intermittently. My observation is that skiing is a polarizing sport. Most people try it once and either quit or are soon addicted. The other key advantage you have is that skiing one or two days a week at short distance daytrip areas you can push harder and progress faster than the person who is on vacation skiing 6-7 days in a row and gets tired, has to pace himself and/or has to take a day off. I was very fortunate to have the still-best 1978-79 SoCal snow season in my learning stage. Thus I did not miss a single weekend from mid-November to early April, so I made great progress over the 30 ski days and was totally addicted by the end of that season.
Season length: 21 months, Nov. 29, 2010 - July 2, 2012
Days in one year: 80 from Nov. 29, 2010 - Nov. 17, 2011
Season vertical: 1,318K in 2010-11
Season powder: 291K in 2011-12