Fate-is-one-edge: Ofcourse they can be carried over. Mind that, you can start an NG+ only by using a regular save. You can't start an NG+ using an NG+ save. In those terms, only one of the rewards can be carried over and you can't have them all at once.
https://www.reddit.com/r/witcher/comments/4qhc5h/gaunter_odimm_rewards_and_ng/
Horn of plenty is a bit useless if you have Blood and Wine DLC, because of the 'Gourmet' trait. The only item somewhat worth it, in my opinion, is the sword, because of the dash and bash moves it allows you to perform. Oher than that, I go for information about Cyri, since that is what Geralt would most certainly choose.
I was expecting to be able to continue the NG+ into a new game, well that's a bummer. I thought it was gonna be like with Mass Effect. Anyway, turns out GoD can't be played, eh?