Bad weather alone wasn't enough to so much as make the barbarians consider giving up on their campaign. But it wasn't just bad weather. A large portion of the warriors, the ones in charge of realizing the campaign, were afflicted with residual ice magic. The bad weather worsened their condition.
They were in no state to fight. They would be lucky if they didn't get worse or started getting sick.
Fighting like this would be impossible. After all, unlike them, Soku could handle the rain. They had roofs over their heads, dry firewood, and shelters for their soldiers, most of whom were uninjured. They also had paved or cobbled streets and gutters and drainage systems to handle the overflowing water the rain poured down.
For the city, the weather was just an 'Oh no, we have a reason to stay inside and play board games or cards!' But for the barbarians, it was a struggle to stay warm enough to digest the food they still had.
