(SPOILERS MAIN) What if Jon stayed at winterfell and was named castellan whilst robb went south!

lets say for this scenario Jon Snow doesn't go north with tyrion and benjen and decides to stay in winterfell and with the war still happening and Robb still going south with his northen army he names Jon as the castellan of winterfell while hes away how do you guys think Jon snow would have dealt with the ironborn invasion and with ramsay/reek.

How would this change the story?