You may model it using poke and bevel tools.
Select the faces you want to put the pattern on and hide the rest of the mesh with Shift+H. Press Alt+P to poke faces. Select vertical edges (select one of them, go to Select-->Select Similar-->Face Angles), then dissolve them (except for top and bottom ones) with X-->Dissolve Edges. Do the same with horizontal ones. You now have the pattern base.
Select all the faces, press Ctrl+B and drag the mouse to achieve the desired patern's thickness. Inverse the selection with Ctrl+I. Extrude and scale faces inwards (E,I,Shift+Z).
Unhide everything (Alt+H), select the pattern except for very top and bottom edges. Go to edge selection and press Shift+E to crease it.
Finally, you may bake created pattern to the low-poly version of your ice cone (bake normals) and apply it as a normal texture.