Movie studios are very proprietary over their trailers. I've seen them taken down an hour after they were put up. Ye others are still up and it's been years. They are fickle on who they go after for copyright infringement.
If the video has "Standard YouTube license" you need to read what that covers. The other licenses they offer are all CC -creative commons
To tell if a video is "share-able", If the video has a "creative commons" license (which is shown just before the description), mostly likely it will have a "share" button. That means the owner has given YOUTUBE permission to allow others to use all or part of it as they wish.
This is one of the reasons you see so many repetitive videos. If I saw one video about The Terminator movies, I saw 100 and most of them were compilations from a bunch of other YOUTUBE-r's videos.
It always stumped me why these were not considered copyright infringement when obvious copying occurred on the site. It wasn't until I learned the Creative Commons license allowed them to do it. There are several types of CC licenses and each one is different. One allows use only if you aren't making money on your use, another allows only with attribution link back to the original, etc.
I also wondered how come Schwarenegger and crew hadn't gone after these post-ers (some videos date back as old as 10 years) for copyright infringement. Perhaps they consider them good advertising, I don't know. But I'd step very carefully in this area.
Movie and music studios are notorious for suing for copyright infringement. You would do well to write to the studio licensing agent and explain your use, and get written permission before you publish. Also, they've been known to change their minds after the see the finished product and then the writer is left with no permission. So, you might want to ask them if you can submit it for their approval as well.
This is "walking on broken glass" territory and the big guys usually win because they have the most money. Good luck.