I also ride my bike to work every day, and I ski patrol at the local mountains on the weekend.
I went camping in -35C two weekends ago, it was great!
One of the hardest things to deal with is condensation and sweat - anything even remotely damp (socks, sleeping bag, boots, gloves) will be frozen rock solid in the morning.
I have no experience of camping in temperatures as low as -35C. However, I have found that camping in Scottish mountains it is much more pleasant when it is in the range 0 to -10C than just above freezing.