There's a couple of aspects to that question.
First, is it legal to put a camera on the outside of your aircraft? If it's a CofA aircraft, most likely not, unless there's a provision to do so in the POH, and the camera is placed/used according to the CofA. If it's a PTF aircraft, you can write that provision into the POH yourself so it can probably be made legal. But in any case it's a murky grey area.
In the Netherlands there have been spot inspections by the aviation police and people have been told to remove exterior cameras. But no tickets have been issued to the best of my knowledge. Furthermore, my club has explicitly forbidden the use of external cameras. Not because of the cameras themselves, but because of people using duct tape or other methods to secure them, and these additional safety measures have caused damage. (Duct tape residu is also very hard to remove, which is a huge problem if the aircraft needs to be repainted, for instance.)
Second, is it legal to put the footage on YouTube? Well, if the material is 100% your own, putting the material on YouTube is definitely legal. Even if the material itself shows you committing an illegal act. But I don't think the police is going to investigate you for having an exterior camera, based on YouTube videos alone. (Although the police have investigated more serious crimes based on YouTube/Facebook videos.)
When things become more complex, is when you start using 3rd party content in your videos. Which happens a lot because your audience will not appreciate listening to engine and wind noises during the whole video. So you might be using 3rd party audio for background music. This is where things get interesting.
YouTube has automated detection of 3rd party content like background music called "Content ID". Which actually works pretty well. When YouTube detects that you are using 3rd party content, they will temporary delist your video, until you either acknowledge that you are using 3rd party content, or dispute YouTube on this. (I do not recommend the latter unless you have lots of time.) If you don't do anything your video will be removed at some point in time, I guess. You also get a "copyright strike" on your account, and multiple of these may lead to your account being suspended or deleted.
If you acknowledge the 3rd party content, then it's up to the 3rd party content owner what happens. Typically the 3rd party content owner will want to make some money from your video by showing ads alongside your video, where the revenue from these ads goes to the 3rd party content owner. In this case, your video may not show on mobile devices, where placing ads alongside the video is not possible. The 3rd party content owner can also ask YouTube to restrict the video to certain geographies, or block the video altogether.
Loads more info here:
https://support.google.com/youtube/t...ef_topic=16579
Third, you need to consider whether it's legal to create aerial footage over a certain area, or of a specific object. This was particularly the case in the Netherlands, where a cold-war-era statue prohibiting aerial photo/videography in general was only repealed last year. But almost every country will still have anti-espionage laws on books that forbid you from making photos or videos of certain military and other strategic installations. So it might be wise not to release footage that was shot over an active military base, or something like that. To be honest, prosecutions because of this are extremely rare, but on the other hand, if you do get prosecuted you can end up in jail for a long time. Use common sense here.