I recently joined Lorwolf and I joined the Icerun Pack and did all the quests they gave me, but now they haven't given me any new ones and I'm not sure how to get more. Am I just supposed to explore and battle now I have finished all my quests?

@Wild64 pretty much. The Campaign is a great place to find food and trinkets, earn xp for wolves and compainions and potentially get wild wolves (randomly generated first generations). You can also do the campaign stories for the other packs (don't worry - the dialogue makes it seem as if you join the other packs, but you will safely remain in Icerun)

Currently doing the campaign is also a great way to earn tickets for the event. There's only a little over 2 days left, but the Murkwood Seasonal quests that are related to the campaign can only be done in the Murkwood areas. Completing the tasks (and very rarely even just exploring itself) will award event tickets which you can use to buy exclusive event items. The ones with this year (2024) in the description will not return next year for purchase, so you might want to prioritise those over the other ones.

@Wild64

Not much I can add to what Gaia said, but to address your question about how to get more quests...the developers have mentioned in the past about adding new chapters to the story line quest, but there is no present time table for it. So as Gaia said you can do the story line in all the other packs and this will enable you to play all of the campaign scenarios which will be necessary for the events like April's Murkwood Event. Also some new scenarios like Rockbreaker Ox in Murkwood become available when you reach a certain level in the Professions.