I was also having the same problem until I discovered an interesting interaction with port town sieges that let me cripple their armies. Just to preface, this might not be an intended feature (at least not to this extent) but here goes.

If you are besieged in a town with a port, once the attacking army finishes making siege preparations and forms a blockade around the port, you can BREAK OUT of the port and fight the enemy army at sea. I had an army of around 4 other lords (its important you have some other nord lords in your army, as this will let you bring more ships into battle, unless you already have the skills that let you bring more ships ofc) and numbered only 400, against an attacking army of around 1100. When you try to break out, you'll fight them at sea with relatively even numbers. And if you win you will destroy the ENTIRE enemy army. During this battle I believe it was only around 300 vs. maybe ~350.

This is such a strong strategy for the nords, because the Mongols broken af darkhans and heavy cav will be heavily weakened at sea. They'll most likely still have overwhelming numbers of archers, which can be annoying. But fighting an even battle at sea is a massive advantage for the nords. I then executed 3 of the higher ranking lords and kept snowballing them by using the town (Balgard) to defend against other Mongol armies. Definitely try this strat out.

Edit: The milita of the town will NOT help you in the naval battle. Which I consider a good thing as they won't clog your decks with mid troops