Svenja married Agnar some time after the attack. She was haunted by many lingering dreams of the attack on the mead hall, and believed that the only way to stop them would be to kill the Uderfrykte Matron, the creature that spawned the Udyrfrykte. Svenja and her husband then set out to find the monster, tracking it to the Jerall Mountains in Cyrodiil.
Unfortunately, they were unable to defeat it. During the events of The Elder Scrolls IV: Oblivion, the Hero of Kvatch confronts the Matron while Svenja's devoured remains and her bow are still in the monster's belly, and Agnar is found dead nearby.
Once the Nerevarine becomes the chieftain, they can talk to Svenja Snow-Song about mead hall business. She will give them options to order mead from Skyrim, and send hunters to collect snow wolf and snow bear pelts.