Ornatrix UE assigns a basic material to the hair, which does not use a texture by default. Probably the easiest course of action here would be to duplicate the base mesh's material, change its shading model to "Hair" and assign it to the hair. In case the UV is incorrect with the native UE hair you can try using the "HairAttributes" node inside of the material use its "RootUV" output to get the proper UV instead of the usual Texcoord material node and sample a texture using that.
Since Ornatrix's "editing hair" uses a different shader than Unreal's "native hair" there are two different materials used by Ornatrix by default. In the end, since the end output is inteded to be the native hair the users are expected to author their own hair materials. We can add some more presets in the future though, making this a bit easier.