Icefish style: clear blood.
The icefish has no hemoglobin or other oxygen carrying pigment. Oxygen dissolves directly in the blood.
The ocellated icefish, for example, has clear blood. It's not very
well understood how or why this is. The red color of most blood is
given by hemoglobin, a protein that carries oxygen along through the
bloodstream to the organs that need it.
The ocellated icefish ("ocellated" refers to the eye-like spots that
make up the fish's coloration) does not have any hemoglobin. Its
circulatory system gets along without it: oxygen, rather than being
transported by the hemoglobin, is fully dissolved in the plasma (the
main liquid element of blood). At those cold temperatures, oxygen
dissolves into plasma more easily, and the muscles of the fish's
circulatory system are able to absorb oxygen directly from the plasma.
That's all helped along by the fact that the ocellated icefish has an
extremely strong circulatory system. It's got a much larger and
stronger heart than most other fish, and pumps blood through its body
at a rate five times greater than the average fish.
Clear blood dragons need it cold and they need to stay cold; the colder the better. The warmer it is, the less oxygen dissolves in plasma and the less they can deliver to muscles and organs. Maybe you can rig some way in which they can dump excess heat into their breath weapon, leaving their bodies colder?
Also, the icefish is kind of sluggish. Your dragons could accumulate an oxygen store in myoglobin - that does not circulate but is part of the muscles. Oxygen stored in myoglobin is how whales can pull off their deep dives. That oxygen storage would enable a one time burst of activity on the part of the dragon.