The 11-16 will work at 16mm on full frame (I used it on the original 5D for a little). Personally, I really like the 40mm f2.8 stm, because I can hand my camera to my friends and get great looking casual/candid shots. For skiing, I really like the 200mm f2.8L ii, it's super sharp and focus is quick, even on the 5d (also used a 1D mark ii N and a 7D briefly). My mom shoots with a 6D, and she uses the 16-35 f2.8L ii, the 24-70 f2.8L ii, and the 70-200 f2.8L. She loves all of them, we just got her the 24-70, so I'm not sure how extensively she's used it, but she loves using the 16-35 for landscapes/indoor travel photos (eg a church interior), and the 70-200 to take pics of my little brothers playing hockey (f2.8 is great for the rinks), lacrosse, and some shots of me skiing. I've played around with tem is well in the same scenarios, and they are all fantastic lenses. Just figured I'd give a little info on the ones I actually have personal experience with.
For star photos, the 16-35 is great. We were both using it on vacation recently, and though I only saw the shots on camera before returning to school, they looked awesome. I wouldn't really bother with IS, you need a tripod for the long exposure shots of stars, and you turn off IS in those situations.
Getting a little off topic, but I know the 135 f2L is super popular on full frame for portraits, and I currently have my eye on the 85mm f1.8 as a potential next lens. It seems to be a good focal length, and a great lens (especially given the price), and would probably pair well with the 40mm for travelling/walk around/candid use. I'm up late studying, so this might not all make sense, let me know if you want me to elaborate on anything, or have any questions about any of these lenses.