Ice hazard on steep footpath/cycle lane

A trickle of water flows across the pavement/cycleway after rain (almost constantly in water). This freezes at sub-zero and leaves a sheet of ice right across the pavement. This is a slide hazard for cyclists going uphill as they are moving slowly. This has been the case for at least three years (sorry I should have reported it before). I think better drainage is needed to diver the flow of water which seems to seep out of the side of the hill. A narrow metal covered gutter across the footpath would be better than the current situation.