I'm probably reading too much into this, but from Dana's perspective, I imagine it's possible to symbolize the time period she knew as having had it's final sunset for her. The sun for her era has set and she'll never see it rise again.
But again, maybe I'm reading it in a light a little /too/ depressing. Sure, that revelation might still have some sinking in to do, but on the other hand, she was probably part of that cryostasis experiment voluntarily and had already somewhat prepared herself for the implications prior to her actual freezing.
It's not that uncommon to relate to tomorrow this way. After night shift, 6:00 AM, although it is already the next day, 'tomorrow' is for me when I get up.
