We live out in Aranda and I cycle to work in Deakin which is about a 23k round trip each day. I didn't have the chance to cycle in the UK (moved out here about 2.5 months ago) but love having that chance here. I haven't done a winter yet but am taking the mindset that there's no such thing as being cold, just the wrong clothes! Bike paths are great and I hardly touch a road all the way (I have to cross only one road and that has a pedestrian crossing).
I do agree that not having a car could be limiting as there are some great parks, lakes and other outdoorsie things to do around and outside of Canberra which you would miss out on if you didn't have a car. In our opinion those parks and so on are some of the best things about living in Canberra. You could get away with a small weekend run around as if you need to get up to Sydney, the Snowies or the coast there are very good hourly coaches (check out Murrays Coaches ...).
All the best