Vista Ultimate supports it with DreamScene
Windows DreamScene Free Download for Windows Vista Ultimate » My Digital Life. None of the other versions support animated wallpaper and you can't install DreamScene in any of them (it can't even be purchased).
To get animated wallpaper in Home Premium (or any other version than Ultimate), you need 3rd party software. I've been unable to find any freeware, but I did find some options that don't cost a whole lot and should work on most systems (though some require additional software installations to supplement the product).
Stardock
https://store.stardock.com/product.aspx?productid=ESD-SDS-459 seems to be the most frequently mentioned. It goes for about $20. You also need to install another software package called Impulse
Impulse Driven : About before installing Stardock and it says "free download" and that you need to setup an account which to me suggests it isn't free (maybe a one time fee or maybe even a subscription) though I didn't want to download it and get caught up in account setup routine to get the whole story. You can check it out if you like - it's almost certain you'll be given the pricing and terms before you need to commit (I just wasn't in the mood because I'd never really use such a product as it's a drain on resources and I almost never see my desktop anyway).
Here's another option DreamScene Video Wallpaper (again $20 but no additional software required):
Animated wallpaper Vista software downloads - DreamScene Video Wallpaper Vista download - Best Free Vista Downloads which claims to be as good as DreamScene for Vista Ultimate but available for all versions of Vista.
There are others if you search: here's a pretty good list:
animated wallpaper vista downloads in Themes & Wallpaper software - Best Free Vista Downloads.
I don't know where you would get the animated wallpapers that would work with these programs - perhaps they all do or perhaps they require a certain format - that wasn't very clear from what I read but I got the impression that free animated wallpapers were readily available and I saw many listings (just not verification they would work with this software - though I'd be willing to bet that's the case though the regular animated wallpaper may differ from the DreamScene animated wallpaper).
Although Stardock offers a free trial, I'm not sure about Impulse or DreamScene Video Wallpaper - I'm not even sure if or what Impulse costs and DVW does not mention any free trial or demo period.
The articles show system requirements and such - I suspect you'll be fine but they do have some requirements (I just imagine you already have them or can readily install them).
I hope this helps.
Good luck!
who unleashed the banhammer? lol