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For water, as for other substances, there is a phase diagram (wikipedia.org), which shows what phase state the substance will be in depending on temperature and pressure. In outer space, that is, in a vacuum, the drop will begin to evaporate intensively, this will lower its temperature, and it will turn into an ice floe or snowflake, and then it will evaporate less intensively, depending on the light, it will either evaporate completely or remain in solid form.
Temperature is the speed (ethergia) of movement of molecules (atoms) of a substance.On the surface of the earth, water freezes because water molecules collide with molecules of the surrounding, colder substance, lose speed (momentum energy). Ice at a temperature of 0K will have no movement of molecules. In space, water molecules flying in different directions will transmit their momentum to whom? Only to the same molecules with the same momentum. The total momentum will not change. And the temperature (speed of movement) will not change. They will fly apart, molecules in different directions and fly to all corners of the universe with the same temperature until they meet someone on their way.