The dragon is not a picture laid over the sky but a way of holding seven star groups in order. Its lodges run Horn, Neck, Root, Room, Heart, Tail and Winnowing Basket, and the names read down the animal from the head: the Horn at Spica, the Neck and the Root behind it, the Room and the Heart at the body, with Antares as the great red star of the Heart, then the Tail curving into what is now Scorpius, and finally the Winnowing Basket in Sagittarius.
Chinese astronomy divided the sky by these twenty eight lodges rather than by twelve zodiac signs, and the divisions are unequal because each is defined by a determinative star and the arc from it to the next. That makes the system a coordinate frame for tracking the moon and the planets, not a decorative scheme, and the four animals are the four groups of seven that the frame falls into.
The seasonal association follows from what is visible. The rising of the Horn in the evening sky belongs to spring, when the eastern palace comes up, and the correspondence of the quarter to spring, to the phase Wood and to the blue green colour is built out from that.
A well known reading connects the dragon lines of the first hexagram of the Book of Changes, the dragon hidden, the dragon appearing in the field, the dragon flying in the heavens, to the constellation's seasonal appearance and passage overhead. It is a proposal that has been argued for a century and remains a reading rather than a demonstration.