Does Ceres belong to the terrestrial-type celestial bodies?
I'm inclined to say no (and footnote, I realize Wikipedia isn't a good source for scientific proof as it's not always right, but I'm using it more to demonstrate a point than than use it as an authoritative definition). Wikipedia:
A terrestrial planet, telluric planet or rocky planet is a planet that is composed primarily of silicate rocks or metals.
All terrestrial planets have approximately the same type of structure: a central metallic core, mostly iron, with a surrounding silicate mantle. The Moon is similar, but has a much smaller iron core. Io and Europa are also satellites that have internal structures similar to that of terrestrial planets.
Dwarf planets, such as Ceres and Pluto, and large small Solar System bodies are similar to terrestrial planets in the fact that they do have a solid surface, but are, on average, composed of more icy materials (Ceres and Pluto have densities 2.17 and 1.87 g cm−3, respectively, and Haumea's density is similar to Pallas's 2.8 g cm−3).
So, in my opinion, half ice/half rock if a different category and not terrestrial. There probably are planets that formed outside the frost line that are half rock-half ice in other solar systems, but I don't think I'd call them terrestrial. We probably need a new word for them.
If Ceres was to drift closer to an Earth's orbit, it's ice would melt and it would have oceans (and an H20 rich atmosphere), at least, for a little while anyway until it lost it's atmosphere. Planets with Ceres composition would likely be water worlds if they were warm enough.
Now, I can't speak for any the official answer, but that's my opinion. If Ceres is Terrestrial and Haumea is more rocky than Ceres, then Ceres probably shouldn't be the only terrestrial dwarf planet in the solar-system.
Link provided that says Ceres is a terrestrial dwarf planet.
Terrestrial planets have numerous similarities to plutoids (objects like Pluto), which also have a solid surface, but are composed of more icy materials.
Some of this is just semantics, but lets look at density, which is a pretty good measure of Water-Ice and other ices to Rock content.
Ceres 2.08 g/cm^3
and the other dwarfs, by size (not all of them are well measured so density isn't certain).
Eris 2.3 Pluto 1.88 Makemake ~2 Haumea 2.6-3.3 Quaoar ~2.2 Sedna (2.0?)
and I could go on.
Lets do a few moons, just for fun.
Io: 3.55 (extreme volcanism) Europa: 3.0 Ganymede: 1.93 Calisto: 1.83 Titan: 1.88 Triton: 2.06 Enceladus: 1.61
Moons are easy, we don't call them dwarf planets even if they are larger than dwarf planets cause we call them moons. - definition averted. :-)
But I have a hard time seeing why Ceres gets a different classification than other very similar objects which just happen to be further away. Now, granted, Ceres, while it formed outside the frost line, it's now inside the frost line so surface ice on Ceres doesn't last. It's got a rocky surface while most Kuiper belt objects have an icy surface. I can see that, defining an object based on it's surface, but I still think a half rock/half ice object (of significant size, large enough to be round and meet dwarf planet criteria), should be called half rock-half ice or whatever that definition is. I don't think it should be rocky/terrestrial if it's Ceres and icy if it's Pluto, even if that's how they look the surface, but that's just my opinion.
/// hope that wasn't too much of a rant. :-)