If the ground is -1° C and a raindrop of +1° C falls on it, will the ground freeze the drop or will the drop thaw the ground?

Answer

In thermal equilibrium (when temperature has become independent of time), the ground is on the winning side. After all, the amount of thermal energy in the ground is much greater than that of the raindrop and the final temperature will not differ much from -1°C. The raindrop can temporarily warm up a part of the soil (especially if it is porous sandy soil), because soil is a poor conductor of heat and it can take a while before the heat is supplied.