Air coming through Windowsills and Floor (pictures)
I agree with the other guys. Just to expand a bit, mindful of the fact that it is a rental, and not knowing what the landlord may or not may go along with, here are a few thoughts that you might bounce off of him or her.
While my guess would be that the walls were insulated, insulation was not as good, nor taken as seriously in the '60's, and what is there has almost certainly settled. This may be able to be corrected by injecting insulation into the cavities through holes on each stud bay, which could then be repaired with relative ease. Before doing this though, I would hire someone to perform a thermal scan, in order to have some idea of how effective this might be.
It does not appear that the window trim has been removed or replaced, so you can be certain that there is nothing around them, so I would probably be inclined to make this a first objective. Depending on your skills, your desire, and your landlord's willingness for you to participate from a cost standpoint, maybe even a trade in part of a month's payment, or something like that (?), it is certainly within the capability of a desirous novice to carefully remove the trim, assess the situation, correct it, and replace the trim, possibly without having to repaint if done carefully, but, if not, repainting would be your worst case scenario. As Joe mentioned, you may very possibly have window weights in there to deal with, but you could post some picture of that at that point, and probably pick up some pointers here.
The rim joists were definitely not insulated at the time of constructon, so, unless the landlord has since done it, these could be better sealed with some rigid insulation and spray foam.
From a much less costly and less permanent standpoint, as Fix'n it mentioned, you could caulk the gaps that you see around the windows, and, as far as the gap along the floor, again, mindful of the circumstances, and as a short-term resolve, I might tuck some backer rod, which you can buy from your local hardware or home center, in there. It is not the "right" fix, but it should give you an idea of how much draft you have coming in that area.
Last edited by DexterII; 01-24-2013 at 10:44 AM.