I booked separately, way last April, and requested NQQ1, 7th floor with as little "tree branch view blockage" as possible.
I called last week, about 4 days before we left, to confirm. Jennifer (so kind and helpful) checked it out for me and was clicking her tongue worriedly, because she said usually they "block out" (i.e. assign the rooms according to availability, requests, how many nights, etc-- kinda like playing Tetris) the rooms a week or two in advance, but they'd blocked out mine in September, and I hadn't gotten 7th floor, although I had one of the earliest requests in. She didn't like that, so she fooled around with it till she could rearrange and get me what I wanted. It was perfect! We had room 1713. There are trees in front of all the windows on that side, but that particular room had the branches mostly to the side, and a straight, unobstructed view of the Matterhorn.
The freeway noise is very noticeable on the balcony, but with the door shut, the room is very quiet. We did bring a white noise machine, which helped us sleep soundly through the early-morning rush hour, which sounded like a far-off rumble. It also helped muffle the sounds in the hallway, where, like any hotel, you get the occasional guest who lets their door slam shut late at night. ("Ka-CHUNK!")
I would call in-house reservations and put in your room requests ASAP.