Oxtoby had called the postponement of the second leg a "challenging day" and fresh snow had to be cleared off the artificial surface at Throttarvollur before kick-off.
It was always going to be a difficult ask for an injury-hit and youthful Northern Ireland to stun the Euro 2025 participants in the second leg, but they pressed forward in the early stages without worrying the hosts' goal.
With Inter Milan's Karolina Lea Vilhjalmsdottir pulling the strings, it wasn't long before the hosts got into their stride
Visiting keeper Jackie Burns, player of the match from the first leg, was called into action to keep out a low effort from Hildur Antonsdottir, and she then denied Glodis Viggosdottir from the resulting corner. 
Vilhjalmsdottir curled an effort just wide from the edge of the area and Sandra Jessen missed a glorious chance when she headed wide from six yards. 
But Iceland took a deserved lead when Eriksdottir beat Caragh Hamilton, and her low cross was touched into the path of Jonsdottir and the Angel City forward hammered the ball into the top corner. 
Northern Ireland had a superb opportunity to equalise on the night two minutes after the restart when Joely Andrews won the ball high up the pitch and found Kascie Weir, but her first touch was heavy and goalkeeper Cecilia Runarsdottir was brave to dive at the feet of the striker. 
But the game was put to bed on 58 minutes as Northern Ireland conceded from a set-piece for the third time in the tie.
Jonsdottir's long throw was flicked on and Eiriksdottir's looping header was beyond the reach of Burns. 
Alexandra Johannsdottir fired over from range as Iceland continued to press, and Gudrun Arnardottir dragged an effort wide shortly after.
Things went from bad to worse on 73 minutes for the visitors when Nadine Caldwell fouled Vilhjalmsdottir in the area, and Asgeirsdottir fired home the resulting penalty.
Northern Ireland ended the game well and some good work by Leyla McFarland and Rebecca McKenna created a chance for Emily Wilson, but her effort was well blocked by Asgeirsdottir.