I don't know what the current state of the art knowledge is with respect to freezing or hibernating people. I think the science-fiction depiction (like in the Alien movies, or Han Solo frozen in carbonite) is generally that a person's metabolism is basically stopped and (optionally) their body is cooled to a very low temperature to stop chemical processes from happening except at a very slow rate. I think it's implied that you don't age at all, and you probably don't consume calories. (The machine you're in just requires electricity to run presumably and maybe has some consumables like IV fluid and drugs.)

If I understand correctly, one of the barriers to the science-fiction approach of freezing people is that ice crystals form and destroy tissue if one were to actually literally freeze a person. In order to survive that, you'd need some way of inhibiting ice formation. Maybe it could be solved by injecting people with some non-toxic antifreeze solution, or immersing them in fluid at such high pressures that ice doesn't form, or you could just maintain a temperature just above freezing. And then there's the problem of how to thaw a person back out. I don't know if that's solved, but I guess there is a body of knowledge around reviving extreme hypothermia cases.

Less extreme forms of hibernation might look like medically induced coma or like a bear hibernating through the winter. I don't know if bears age significantly while they're sleeping. I'd guess that they age somewhat, but at a slower rate than normal.