If they managed to hold out until a serious snowfall, the force outside would be forced to abandon the siege or would try and storm the walls and gate again. They couldn't really keep the siege going when they were unable to keep the supply train in the snow. And if they did hold out until winter, old Roose would still not let a rebellious House off so close to Winterfell and would descend upon Ironrath in strength. Holding Ironrath with 80 men against six hundred outside was doable, but if a bigger force came, they would fall.