Slow positrons are generated from a 22Na source and cone-shaped solid neon moderator and extracted as a magnetically guided beam. Measurements are presented for the mean parallel and perpendicular energies and the radial distribution of the beam particles. Over a distance of 7 m, where the magnetic field B varies from 0.005 to 0.12 T, the beam transport is found to be adiabatic for mean energies up to 50 eV. Non-adiabatic effects, evidenced by an increase in energy in motion perpendicular to B, are observed at larger transport energies. The implications of these observations for buffer-gas positron traps and other positron-transport beamlines are discussed.