This is not a novel, but "longish" short fiction, novelette or novella. I read it around 1984, in an already used book containing half a dozen or so stories, in a cheap hotel in the US. There were several such books on a shelf, there. I also read another, very similar one, that contained "Nightwings" by Robert Silverberg. After checking all collections containing the latter published before 1985 (thanks, Jenayah !!!), I got to the conclusion those were two different books. It is not a bad story, but it did pale compared to "Nightwings" !
A man, on our Earth, is contacted by a bizarre agency who offers him to get his mind transferred to a body in an alternate Earth, in order to save, either some polity from an external enemy, or the queen of some polity threatened by an "internal" cabal, I forgot. Why he accepts is not clear, since when will he be able to use the money he is offered? No return seems promised.
He gets there, and meets several species of humanoid beings. They all have names that contain the word "man" in the local language, but I forgot how that sounds. One species is a "snow-man", a huge and frightening Yeti (but not the most agressive species in that world) who lives in the eternal snows of a high mountain range (or, possibly, of a polar cap, I forgot). Another is a "Cave-man", without eyes because they live in deep caves with no light. A third one is amphibious, "Water-man" or "Sea-man" or "River-man", I am not sure. One species practices cannibalism, and they file their teeth better to tear flesh. I forgot if it is one of the latter two, or still a fourth one. Finally the ones he is supposed to help are essentially like us.
Our hero crosses all these obstacles, reaches the polity he has been hired to help, and saves the queen from the cabal, or possibly the entire polity from the enemy. I don't remember the end well, but he never goes back to our Earth.
