I've never heard of any law that required a tenant to fix drafty windows.
You could ask the landlord to fix them though but if the apartment is warm and at a livable temperature then there's probably not much you can do if the landlord doesn't want to fix the drafty windows.
Maybe get some heavy curtains and put the curtains up over the drafty windows.
I do that at home. I put heavy curtains or even blankets over my windows to help stop the drafts when it get really cold outside.