The framing on an addition is the fast part. A one-story addition can be framed and sheathed in a week or two. What takes time is everything before it: engineering, permits, design review where it applies, and getting the foundation in before the ground freezes.
Start with the county. Pitkin, Eagle, and Garfield each run their own building department with their own submittal requirements, and Aspen and Snowmass Village add design review on top. Your builder should tell you at the estimate which jurisdiction you're in and roughly how long approvals take, because that sets your start date.
Next is the connection to the existing house. Additions fail where new framing meets old. We open the wall early to see what's actually there, tie the new foundation and framing into the existing structure the way the engineer drew it, and plan the roof intersection so snow and meltwater have somewhere to go besides into the seam.
Then the season. Concrete wants warm ground, framing wants dry weather, and the valley gives you both for about six months. A good schedule pours footings in late spring, frames through summer, and has the addition dried in with roofing and wrap before the first real snow. If a builder promises to start a foundation in November, ask how.