I've seen several suggestions as to how to nerf the snake (most unreasonable, as killing a card that an entire archetype is built around is as bad as making it too strong).
I have thought about how to change the card, and what the problems are with it. Most people seem to want to lower its amount of Health stolen, but in the matchups where it is really strong, I don't think dropping it to 8 really changes too much.
What I think they should do, is just make its effect go off at end of turn, rather than be a battlecry. This would, in very niche situations, make it stronger than it is now if it lives (very, very unlikely to ever happen). But ultimately, removes the ability to bounce hold a wincon off of it.
This preserves the initial intent of the card, being an instant 20 Health swing, while also removing it's un-interactive aspects.
I think increasing the cost would be enough. That would buy a lot of time which gives decks time to pressure or draw into hand disruption. It's only really annoying right now because they can play it 3 times by like turn 8.
I doubt they're going to increase the cost considering all the azerite legendaries are 4 mana 5/5. no need to break the theme and increasing the cost doesn't really fix the issue. Reducing it to 5 damage or honestly just a complete rework would be better. It's an incredibly unhealthy card for the game in its current state regardless of how good it is, because as long as it exists control or combo decks will be significantly worse. It's either aggro, or warlock.
i mean why is it not just a normal lifesteal? the reason its so busted is because it actually takes away your max health, there is absolutely no way to play around it. at least if it was life steal yo ucould heal back up.
I think the main problem with the Azerite Snake is the "steal" part. So my best bet it that they'll nerf it to just deal damage instead (probably with lifesteal) and bring it down from 10 to 5, but your suggestion is also very likely that it will be an "end-of-turn" or "deathrattle" effect rather than a "battlecry" to stop or at least slow down the combo and give the opponent the possibility to clear it.