The property you are renting does not belong to you, and therefore you cannot make any permanent changes to it, including weatherization. You can be sued, evicted, and forced to pay the cost to restore the apartment to the way it was before.
I doubt you can make the landlord do anything that is not within your lease
what is weatherian? In guess is was just dumb, I googled it and nothing comes up. So please learn to ask a question.