All you need to do is move your save game to the cloud to not lose progress on the XB1.
As stated above:
Go into "Storage" on the 360 and move all the FH1 files that are classified as "Saved Game" to the cloud. There are about 5 or 6 of them, including the actual save file as well as saved photos, setups, etc.
And any DLC content will be available to install when you go Manage game on the XB1.
Thanks ☺ Although it's installing to my XB1 now and has 9.6GB which was the exact size of Horizon on my 360 including DLC so we'll see...