Is it common to see some eye floaters when looking at the sky?

Yes: They are either tear film components or blood cells of retina being seen.

Yes, sometimes: Floaters are due to imperfections in the clear gel inside the eyeball, and tend to become noticeable as a person ages. Floaters occur in many people, and sometimes are more noticeable if one is looking at a plain blank surface such as a blue sky. Large numbers of floaters, noticeably increasing floaters, flashes of light, changes in vision, etc..., should be evaluated by an md eye doctor.