Winding, sinuous, serpentine, tortuous, flexuous can all mean curving first one way and then another.
Winding , the general and the ordinary term, often implies spiral ascent. When applied to things in a horizontal plane it implies little more than weaving from side to side or in and out through some length, often without apparent plan.
Sinuous fundamentally suggests frequent departures from a straight or direct line by curving. In its extended use where it may imply moral deviation this implication remains strong, but in respect to material things the word tends to stress the presence of curves in every line, bend, and movement and the absence of angularity, awkwardness, or stiffness.
Serpentine implies curving in a pattern suggested by the smooth and flowing curves of a moving snake; it need not imply regularity in the size and shape of the inward and outward curves. As applied to a type of compound curve or to the front of a bureau or sideboard having such a curve the word implies that the bulging or convex curve is in the center.
Tortuous , like sinuous, suggests lack of straightness and directness, but in contrast it stresses the number and intricacy of bendings, twistings, and turnings rather than the constant flow of curves.
Flexuous, commoner in technical than general use, basically suggests alternation of gentle opposite curves or an easy zigzag course.
In extended use it implies a lack of rigidity in action, and so comes very close to flexible .