You must control a defending character at the point when you would trigger the reaction, not at the point when the winner (and loser) of the challenge is determined. For instance, if Drogon (R) kills your only defending character first, The Bloody Gate’s reaction can no longer be triggered. Same thing if you use Ser Vardis Egen before triggering The Bloody Gate.
Cards like The Haunted Forest do not count as defending characters, even if it means the challenge is opposed. On the other hand, a character that is participating in the challenge as a defender but contributes no STR to the challenge (due to Balon Greyjoy (Core), for instance) does allow you to trigger The Bloody Gate, even though the challenge is considered to be unopposed.