Don't have an answer on this one, I've got a "pretty sure." Not good enough for me:

My opponent declares an attack with Feral Rage. I say "Entangle!" (before he exhausts for the attack), Stretch exhausts and I discard a card (as per the cost of the card). Does this prevent Feral Rage from attacking this turn, since he's now exhausted?

Yes, as long as you do it before FR exhausts (must be performed during attack declaration)

The reasoning behind it working is at the point you play the Entangle, FR is just a proposed attacker.

Using Entangle this way is really non different than a good Doom player using MP.

I mean what if he proposes an attack with FR that you don't mind happening. You would have wasted an Entangle if you used it earlier.

Good. That's exactly how I thought it worked. Thanks!