Measurements of the order parameter texture of rotating superfluid ³He-B have been performed as a function of the applied azimuthal counterflow velocity down to temperatures of 0.2 T _c. The results are compared to the hydrostatic theory of ³He-B. Good agreement is found at all measured temperatures and rotation velocities when the flow anisotropy contribution to the textural free energy is adjusted. This gives a superfluid energy gap Δ(T) which agrees with that measured by Todoshchenko et al., with Δ(0)=1.97 k _B T _c at 29.0 bar. The B-phase susceptibility, longitudinal resonance frequency, and textural phase transition have been extracted from the measurements as a function of temperature and azimuthal counterflow velocity. Owing to decreasing absorption intensities the present measuring method, based on the line shape analysis of the NMR spectrum, loses its sensitivity with decreasing temperature. However, we find that in practice the measurement of vortex numbers and counterflow velocities is still feasible down to 0.2 T _c.