Should I put weather stripping on my unsealed windows and doors?
If your leaking problem is from loose fitting window sashes or a poor fitting door, the simplest and cheapest method would be to purchase some self-adhesive foam weather stripping. This rolled product can be easily installed at the bottom of a window or around the outside edge of the door frame. Select the smallest size that will help seal the gaps, then just peel and stick. Too large and you may have difficulty closing the door etc. 

Another good window treatment is the clear plastic window film like the 3M Indoor Window Insulator that mounts to the frame of the window. Use a hair dryer to "stretch" the film, thus sealing any air leaking in around the sides or through poorly glazed panes.  

All these products are cheap and available at any hardware store or box store like Lowe's or Home Depot.  Stay warm!