Hi, I am not a dane neither i have very good dansk skills. But according to a danish grammar book, reflexive pronouns are used when the subject and the object are the same person.[...]
In this case, MAYBE, the meaning of the sentence does not mean "he rests himself" or "he rests", like to have some quite time, in which case "sig" would be necessary. Maybe the meaning is like the 2.a or 2.b of ordnet: http://ordnet.dk/ddo/ordbog?select=hvile,2&query=hvil
Please don't take this as a correct answer, but maybe it brings some useful information.
I spoke to a Dane about this. Both vi hviler (we are resting) and vi hviler os (we are resting ourselves) are correct, but vi hviler os is more commonly used in conversation. Similarly, instead of han hviler (he is resting), you could also say “han hviler sig (he is resting himself)”. The reflexive (os, sig, etc) is sometimes used for emphasis of the sentence, but otherwise still has the same meaning as without the reflexive.
Sometimes when I have usage questions like this, I search in Google books with the words in quotes. Searches for "hun hviler", "han hviler", and "vi hviler" turned up cases for all of them with and without reflexive pronouns.
"Vi hviler os og hører lidt musik" We are resting and hear a little music "Vi hviler i øjeblikket" We rest in the moment "Han hviler sig lidt" He rests a little "Han hviler blødt" He rests softly
So I didn't see a definitive usage pattern, but that is likely complicated by the fact that "rest" can be used metaphorically such as the "rest in the moment" example.
They make sense to me. "We rest the horses" is a present tense version of something like "After a long ride they rested the horses". I suppose it might make more sense as "We are resting the horses" (because they have been ridden a lot recently), or "we are resting him" (fx. a sports player who has been injured), but they are still understandable to me.