I practice a general rule for myself: if it's below freeing outside, I don't fish with a bamboo fly rod. If it's cold enough for ice for form in the guides, I leave the cane rod at home & fish with a fiberglass or graphite rod.
Very cold temperatures will make any fly rod more brittle & susceptible to breaking - especially in the thinner tip area of the rod. There's less material there to support itself & a lot of bending takes place in the tip. In fact, the best way to remove the ice from a tip top guide is too warm it up & melt it with the heat from your hand gently wrapped around it. Don't try to pick at the ice in the tip top.
Bamboo fly rods are very tough & can take a lot of abuse, but you can never be sure how the cold will effect them. Actually, they're fine just sitting stationary in the cold, it's when you start to flex them or put the weight of a heavy fish on them that you have to watch out. Unlike other rods, bamboo fly rods are laminated. Since you don't know how the cold can affect the glue that's holding the rod together, it's best not to put your cane rod through a tough workout on a very cold day.
I know that this is most likely overkill. Bamboo fly rods have been used in some of the coldest conditions to catch huge salmon & steelhead for over a century. Still, if you have a special bamboo rod that you love, why take an unnecessary chance? Besides, there are plenty of really great fiberglass or graphite rods to fish with, too. Just some food for thought to all you winter warriors out there.