ha ha ha ice bullet!
lets take away the whole firing it from a gun and just somehow have a magically flying high speed bullet.
First off, ice is 1/10th the density of lead, so this means much more surface area exposed to air, hence you are going to bleed velocity like crazy.
Second, as ice is so much lighter, even fired on the moon where there is no air to slow down the bullet, it is so light that it will have to go MUCH MUCH faster than a lead bullet to deliver an equal energy load to the target.
Ice, even Pykrete which is much stronger, is still not nearly as strong as lead, and we all know that varmint bullets need to be carefully constructed so that they don't fragment when flying at velocities in teh 3500 fps range. So if ice/pykrete has to go say 10,000 fps to have equal energy of a same sized 223 projectile, I just don't see it holding together. Even if it does, it won't be going 10,000 for long, it will drop velocity extremely quicky.
As mythbusters pointed out, using a large caliber handgun very very close would work...but so would stabbing someone with an icecycle.
The other option is to have a much much MUCH large than average ice bullet, this will allow it to have much lower speeds due to it's great weight. Also, with a 3 dimensional shape, ratio of surface area to volume decreases as size increases. Take a 1cm on each side cube, volume = 1cc, surface area = 6cm. 1cc volume = 1gram weight Each gram has 6cm squared exposed surface
Take a 100cm on each side cube, volume =1,000,000cc surface area = 60,000 each gram now has .06 cm squared exposed surface.
Hence the other option would be to get a 'bullet' the size of a large cantelope, this would allow sufficient mass at low velocity to do serious damage, as well as sufficient weight/surface area to retain it's original velocity for some period of time.
ladies and gentlemen, I suggest the ICE TREBUCHET! if you miss with that, run up and stab them with the icecycle. Remember, if you suck on the tip for a few seconds it can get very sharp.