In a well done suspension, the damage from oxygen deprivation should be minor. In a more perfect world, the suspension procedure would be able to start before legal death, which should reduce the damage from ischemia even more because there wouldn't be any time when the heart is stopped and the body is warm. Thomas Donaldson says that brain waves of supercooled small animals have been measured, and there are none, even though the animals still have their memories after they are rewarmed. He cites AU Smith, ed. Repairing the freezing damage looks much harder than curing any existing disease, so if revival is possible then curing the disease ought to be trivial.
Old age is a disease that ought to be easier to cure than the freezing damage.
Straightforward chemical arguments lead to the conclusion that significant amounts of decomposition do not occur at liquid nitrogen temperatures. This isn't true for either dried or embalmed tissue kept at room temperature. Also, Alcor and Trans Time have done experiments with dogs that demonstrate that part of the suspension process does not cause damage. Dogs have been anesthetized, perfused with a blood substitute, and cooled to slightly above 0 C for several hours. After rewarming and replacing the original blood, the dogs revived with no obvious brain damage.