I want to drink the coffee cold.
I don't want to eat the soup cold.
Quite a lot of times I've come across such a sentence in which people wrote "drink it cold" or "eat it cold", but I have no idea how to classify such a cold into a grammatical element. Are the colds above used as a postpositive adjective, or just object complement as in the sentences right below? However, 'drink' and 'eat' seem to be different from thr verbs of the three sentences below in that there seems not to be implied or omitted "to be" in between "the coffee and cold" and "the soup and cold" unlike below sentences, in which "to be" can be considered implied or omitted.
I want the coffee (to be) cold.
I prefer the coffee (to be) cold.
I like the coffee (to be) cold.
I think in both cases drink and eat seem to have a similar construction to the verb 'feel' as in
I'm feeling his body cold.
So, I presume both to be used as an object complement that needn't to imply "to be" before, but I'm not sure.