Hamsters can indeed be frozen to death in a low-temperature environment, which mainly depends on the environmental temperature and whether the warmth-keeping measures are in place. Here is the key information sorted out:

The Critical Temperature for Freezing to Death
When the environmental temperature remains below 10°C for a long time, hamsters may enter a state of pseudo-hibernation due to the cold. If they are not rescued in time, they will die.
If the temperature is below 5°C, the physiological functions of hamsters will decline rapidly, and eventually, their organs will fail due to heat loss.
The Difference between Pseudo-Hibernation and Death
State of Pseudo-Hibernation: Hamsters will curl up their bodies, and their heartbeats are weak but detectable. They need to be given first aid by raising the temperature (such as using a hot water bag or an electric blanket) and supplementing nutrients (such as glucose water).
Characteristics of Death: The body is stiff, there is no heartbeat, and breathing has stopped. At this point, it is irreversible.
Preventive Measures
Temperature Control: The optimal living environment temperature is between 20°C and 28°C. In winter, it should be kept between 18°C and 26°C. Avoid using ceramic nests (cotton nests or thickened bedding materials are recommended).
Diet Adjustment: Increase high-protein foods to help hamsters store fat to resist the cold, but avoid overfeeding, which may cause internal heat.
First Aid Methods
Rapid Rewarming: Use a heat source of about 55°C (with a towel in between) to warm the hamster's body, and continue for about 20 minutes until its limbs start to move.
Nutritional Support: After the hamster wakes up, feed it electrolyte water or rice paste to avoid choking.
If a hamster has no signs of life for more than a few hours, it cannot be saved. It is recommended to reduce the risk by observing the hamster's behavior and regularly checking the environmental temperature.