Wool has a fantastic way of retaining loft which in turn maintains dead air space and will retain 90% of its insulating power when wet but it won't compress worth a hoot when it is time to stow and it never rains here. Most importantly, it will rarely be below 40 degrees on my morning commute. I'm thinking my approach will be more to block the wind I will generate rather than use thick clothing but I'm not really sure.
I am an experienced backpacker but dressing for the bike is an entirely different game I've discovered.