A cuckold is not the "cheater". The nature of the "classic cuckold" is his wife has sex with any male she chooses. Her husband becomes a servant of sorts who may watch, he may be humiliated by his spouse and her lover, or he may be forced to submit to both in order to have some sexual release, whether with her or alone with her permission.
I'm sure that's correct in the context of this discussion, but my understanding of the word cuckold is "a man whose wife has sexual relations with another man or other men, without his knowledge".
I'm not sure what to call it where the husband willingly participates in the practice, and, presumably, gets a kind of ambivalent thrill from it but I don't think it's properly called cuckolding - Hot Wifery, perhaps.