Which model is it, they used two types of shutter. It sounds like the older cloth type. I've had similar happen with a Pentax KX which I then stopped using, miraculously when I tried it again a year or two later it worked fine, and is still OK..
Stick the camera in a warm place for a few days it's just possible the cold has affected the lubricants and the shutter curtains dragging, you should be able to see the problem with no film & the back open if you fire the shutter off a few times.
Ian