First, the pavement is not designed for snow-clearing machinery. In addition, there is no system in place to provide adequate water drainage. If the paths were cleared, the snow on either side would create dams where large amounts of water would pool on mild days, creating large patches of ice when the temperature drops below zero.
For the safety of users and to ensure the longevity of the paths, they are only cleared on the portions where there are no sidewalks. Most of the trails that are not cleared of snow in winter have a sidewalk nearby.