Convection is the transfer of heat from one place to another via the movement of fluids. It happens from higher energy level to lower energy level to bring equilibrium to the system.
For vertical set up , if the hot water is places on top of cold water, direction of convection will be from top to bottom. So, gravity can play a role in increasing the rate of flow of energy. if the cold water is places on top of hot water, direction of convection will be from bottom to top. So, gravity can play a role in decreasing the rate of flow of energy.
for Horizontal set up, when hot and cold water are placed side by side, gravity will not playing a role in the flow of energy.So, the position of hot or cold water would not matter.