Let's say I have a Live CD containing Tails that I use to connect to the Tails website. I see a new stable version has come out and want to download the ISO. Can I do this through Tails (through Tor), or is it too dangerous considering the risk posed by rogue exit nodes?

Yes, it's fine. You will, of course, be using your trusted copy of the Tails signing key to authenticate your download. So there's nothing* a malicious node could do to the .iso which you wouldn't be alerted to.
* That's assuming the operator of the node doesn't have a workable attack against the SHA1/PKI scheme. None are known. If such an attack was "doing the rounds" we'd all soon know about it!