If I use Ice to Kill Tywin Lannister with my Edmure during a military challenge when I was the defender does Tywin still win the challenge as he is moribund or is he dead before resolution and the counting of strength ?

Toqtamish said:

Moribund cards go to the dead/discard pile at the end of the action window. That means that action when you used Ice.

So he was dead before the challenge finished then. Good, that means I won that challenge, and that we ruled wrong, oh well still won the game despite that.

Good rule of thumb:

When something leaves play, the only things that can be done while the card is in moribund are Responses. If you get to a point in the game where something other than a Response happens, including framework effects, well, "Elvis has left the building."