How does hibernation reduce risk of radiation-induced mutation?
This is still an area of active research, and there doesn't appear to be a single definitive answer for the mechanisms behind the reduction in radiation-damage during hibernation.
A recent review by Cerri et al. (2016) covers a lot of the known biology behind hibernation and resistance to radiation damage.
A few select quotes from this review:

At the cellular level, it is well known that cells irradiated in
resting state, and left undisturbed for 24 h after irradiation, are
more resistant than cells re-plated immediately after exposure. This
effect is known as delayed plating, and is generally attributed to the
potentially lethal damage repair (PLDR) in resting phase.
...
The oxygen level during hibernation may contribute to the enhanced
radioresistance. Hypoxia is a well know protective mechanism, and is
arguably the main reason of local control failure in radiotherapy.

Rockwell et al. (2009) discuss the underlying reason behind reduced radiation sensitivity in a hypoxic environment:

Molecular oxygen (O2) is a potent chemical radiosensitizer. This
radiosensitization does not result from any of the metabolic or
physiological effects of oxygen, but instead reflects the fact that O2
is an extremely electron-affinic molecule that participates in the
chemical reactions that lead to the production of DNA damage after the
absorption of energy from ionizing radiation [21,22].

My personal take would be that the reduced risk of radiation-induced damage is probably not due to the structural arrangement of DNA, but rather the overall cellular environment. This is perhaps linked to an enhanced ability to repair damaged DNA, but is also likely to be highly dependent on cellular oxygen levels.