My house was built in the 40's. It is in upstate New York. There is a draft in the bedrooms where the exterior wall meets the floor, which is hardwood. I can think of several ways of sealing the draft.
Use transparent caulk where the baseboard meets the wall and where the baseboard meets the floor.
Temporarily remove the baseboard and do something more effective -- perhaps paint with something like mastic or flexseal (having first put down masking tape), or perhaps somehow install a strip of some sort of tape or barrier sheet to cover the line where the wall meets the floor. Put the molding back.
We are thinking of getting rid of the hardwood floor and replacing it with laminate, because the floor is uneven and creaks and squeaks something crazy. If we do this, maybe there is some special procedure to be done after removing the old floor and before putting in the new laminate.