The Spine editor does the triangulation (stored in the Spine data) so runtimes don't have to. The triangle order does matter: Spine sorts triangles based on the order of bone weights and that can be important when a mesh overlaps itself:
http://esotericsoftware.com/spine-weights#Triangle-order
Mesh vertices (and other vertex attachments, like clipping or bounding boxes) in Spine data are clockwise by default, but vertices can be moved in Spine in such a way that makes the winding counterclockwise (eg scale the attachment -1 on X or Y). Attachments defined in old versions of Spine may have used a counterclockwise default (and that winding remains even when saved with newer versions). Runtimes can make the winding order consistent, but this may not be desired if backface culling is on.
The order of path vertices is different from other vertex attachments, it determines the start and end of the path.
