Graphene subject to a strong, tilted magnetic field exhibits an insulator-metal transition tunable by tilt-angle, which is attributed to the transition from a canted antiferromagnetic (CAF) to a ferromagnetic (FM) bulk state at filling factor \nu=0. We develop a theoretical description for the spin and valley edge textures in the two phases, and the implied evolution in the nature of edge modes through the transition. In particular, we show that the CAF has gapless neutral modes in the bulk, but supports gapped charged edge modes constructed by the binding of a vortex (meron) in the bulk state to a spin twist at the edge. The energy gap of this edge mode is therefore dictated by the bulk spin stiffness. At the transition to the FM state where the latter vanishes, the charged edge modes become gapless and are smoothly connected to the helical edge modes of the FM state. We further discuss possible experimental consequences.