A rear drive assembly for a snow bicycle includes a body adapted to be supported by an axle which rotatably supports a rear wheel of a bicycle. An upper arm is rigidly affixed to and extends upwardly from the body. A lower arm is rigidly affixed to and extends at an angle downwardly and rearwardly from the body. A track tensioning and guide assembly is positioned at the remote attachment end of the lower arm. An extendible and retractable attachment member is positioned at a remote attachment end of the upper arm and is, preferably, attached to a seat post of the bicycle. As the bicycle begins to ascend a slope the attachment member retracts to maintain the track in ground contact and as the bicycle begins to descend the slope the attachment member extends to maintain the track in ground contact.