if you can propel a liquid with such velocity as bullet, why not use it to propel solid object with more mass? you get much more damage out of it.

the simplest but still not very small (and very dangerous) is to use a railgun method of acceleration. of course you need some metal (like a small pin) to be in the ice, but after that, ur good to go.

the thing is due to terminal velocity and normal drag force applied by the ice surface, the range of the bullet wont be far.

but what if it was very impure water, like some substance holding the water together, imagine those small jelly water balls travelling at 300m/s. they hold shape better. and they definitely dont leave a damn trace.

bit of calculations : max initial velocity of a 4mm jelly ball. (rough est.)
=sqrt((2x9.81x)/(1.184x4xPix0.004^2))
= 287.03 m/s
~bout 260-270m/s (max initial velocity) after taking into account drag constant.

so, it can travel bout...(wil update later,too complex calc)

so my idea fails anyhow, you have to be too near. damn. back to the drawing board.