Depends on the temperature. At Earth-like temperatures, yes, it would. The transition between the two is around 175 K, give or take; below about 150 K ice is quite stable in a vacuum even over astronomical timescales; above 200 K it sublimates rapidly. (Surface liquid water is never stable in a vacuum or thin atmosphere regardless.)

The rate of evaporation ramps up exponentially, from ~irrelevant at the bottom of that range to fast at the top. (For a body of this size, any resulting vapor would be quickly lost at these temperatures, so the rate of evaporation is effectively the rate of water loss as well.)

This is why Jupiter can have icy moons (temperature ~100 K), but ice sublimates quickly on Mars (~200 K).

Going from a liquid to a gas takes energy, which rapidly lowers the temperature of what remains. Net result most of the water freezes without some external energy source. Sublimation then lowers the temperature of the ice until near absolute zero, again unless there’s some external energy source.

i knew there would be someone to just try to get out of the answer by failing to just go with the spirit of the question by being pedantic. even my own attempt at dispel pedantry just allowed for even more pedantry.