My guy and I just finished bicycling clear across the U.S., and we had no bicycle touring experience beforehand. However, we are both backpackers and, in the end, transferred over a lot of our backpacking philosophies into the bike tour.
I get cold really easily (unfortunately), although I love being in cold climates. I never wore padded bike shorts or knickers--well, I tried, but really didn't like them--, so warm pants (Sugoi, fleece-lined Mid-Zero pants) worked fine when it was cold. Not to mention, a base layer shirt (SmartWool lightweight) and my MontBell UL parka provided just enough warmth on top of the internal heat generated from bicycling-itself (though I only wore the parka in camp or walking about).
I wore lightweight hiking shorts and a tank top on the bike when it was warm so, naturally, this transferred over to other activities perfectly.
The pieces of gear that I relied on the most were my wind shirt (Patagonia Houdini with hood) and a buff for around my ears (fits nicely under the helmet). When the wind was super frigid, I would wear my buff and put the hood up from my wind coat, then put my helmet on; this was a quite comfortable and toasty solution. I also had another buff for keeping around my neck while the other lived across my ears on my head; this buff could also be pulled up over my chin and/or nose and mouth when really cold.
By the same token when off of the bike, the base layers, UL down coat, wind jacket, and buff were really all I needed for most of my body when hiking and camping.
For my hands, when cold, I wore my bike gloves (Specialized BG gel, fingerless) and put my Marmot power stretch gloves over them. For my feet, I LOVE DeFeet Woolie Boolie socks for warmth. Otherwise I just wore my Injini synthetic toe sock liners.
No special bike shoes, only Salomon TechAmphibian (love their ability to turn into camp shoes, how breathable they are, and their ability to turn into comfy hiking shoes). These are more of a 3-season shoe, so for winter I would go with a more tightly knit shoe solution that you could also hike in.
Other than the bicycle, panniers, helmet, and the bike accessories (lights and what not), I found that clothing-wise, all of my backpacking gear worked just fine. True, my bum had to toughen up to the rigors of being in the saddle for thousands of miles, but it all worked out just fine and dandy.