Is it possible to code an animation into hardware?
Getting things to run fast enough for HD video is apt to be difficult, but if somewhat-cartoonish or lo-res video would be okay (e.g. 320x200 at 30 or 60fps) the hardware would probably not be overly difficult.  Standard video requires about 16,000 lines/second; if each line is 320 pixels and each pixel is one byte, that's 5,120,000 bytes/second to read out the data as it's being displayed.  I think an SD memory chip could do that.  If each frame were read twice, every second would require a little under 4 megabytes of data.  A 16GB chip could hold over an hour of uncompressed video in such a format.

If you want higher resolution video, you're probably going to either need much more complicated hardware, or a means of streaming data much faster.  One possible approach might be to use a bank of SD cards, wired in such a way that data can be read in parallel from all of them.  One conceptually-simple way of doing that would be to build three circuits, one for each of the three signals in component video, and have each circuit read off its own SD card.  If one used 4-bit data for each of the components, one could then display 4,096 colors at twice the pixel rate as one would otherwise have displayed 256 colors.