Horgan, who turns 27 on July 18, has been involved in both the Lions' first and second Test losses to New Zealand, but has failed to fight his way onto the starting line-up for this weekend's Eden Park encounter, even though he impressed as a substitute against Auckland on Tuesday.
He has however, made the Test bench, along with Ireland colleagues Shane Byrne and Ronan O'Gara.
Having made four changes across his backline, Woodward admitted: "It (the selection) was very tough on Shane Horgan, who I was thinking about starting with - as well as Shane Williams and Jason Robinson.
Nothing against Robinson or Williams, I just believed these two players (Geordan Murphy and Mark Cueto) deserved a go. I am looking forward to seeing Cueto having a go, he is certainly one of the form European wingers, and he now gets his chance on the biggest stage.
"It was a case of getting everyone well-rested and just making the right calls after the Tuesday night game against Auckland," added the former England coach, who has admittedly put out his "strongest team" available.
Geordan Murphy has had a very good tour, and he was genuinely unlucky not to be included in one of the first two Tests, and I think the same applies to Cueto, especially the way he played in midweek against Auckland.
"I think considering we were 2-0 down in the series, it was right to give a couple of players the chance who had been performing very well."