I live in an old house which I have fixed up a lot. I find it very drafty and can even see frost lines around the old windows where the wind blows in. Will changing the windows fix the problem?

It sounds like you may have a pressure problem. That is to say you have a lower air pressure inside the house then on the outside. One common problem I come across is a lack of fresh air in the furnace room. Sometimes people install a new furnace without introducing outside air to feed the furnace. The furnace uses up air in the combustion process and vents it outside through the chimney. After a while the air in the house becomes depressurized and in older homes you start to feel and even see the cold coming in around the cracks. I would check this and even remove the trim around the windows on the inside and spray foam before changing the windows, especially if the windows are functional. Chances are the drafts are coming in around and not through the windows so simply replacing the windows may not entirely solve the problem.