I’d like to ask if the cold weather froze my hamster’s toes, and what I should do about it.

Based on your description, the hamster’s black, swollen paws could indeed be frostbite. When paws are exposed to cold for a long time, poor blood circulation can cause ischemic necrosis and blackening.

If possible, take the hamster to a veterinary clinic, as amputation may be needed in some cases to protect other tissue. If a clinic visit isn’t convenient, disinfect the paw at home; it will gradually dry out and eventually fall off on its own. During this period, fit the hamster with a collar to prevent licking the area and causing infection.