It also depends on the industry you are in as well as the type of animator you are. If you are in, say like a video game industry where you draw up concepts and scenario's, I would say it's a somewhat stable job (really need to dig deeper, but it's on the more stable side).
Digital artist's doing CG work are in a bit of demand also. Advertisments and stuff usually have artist's who mock up general idea after which it is redone in digital etc.
All in all, you could say this is a custom job with very different requirement and very different condition's unlike established position like management, engineering and doctors. Do a full complete research and weigh the pro's and cons.
In any case, the path for artist's is usually tougher than for the other profession.
In my personal case, I wanted to become a artist but in a third world country like India, that is no way gonna help you survive. Doing something you love will only take you so far. Architect would have been a good choice, but something I didn't risk either. Medical (you get to do tons of drawing, though a very bad reason to study medical for) was too expensive, so I went with the safest choice for me, engineering.
And I am generally happy with it. My pay in general is good and I have enough left to spend on drawing tools to keep it going as a hobby. So while I do like drawing, I have kept it as a hobby and in a position where I would probably never hate it.