The old standby for this was "temporary storm windows", for houses that lacked custom-fitted storm windows.
A storm window overlays the window frame on the outside to prevent exterior air (along with rain, snow, etc.) from directly contacting the single-pane sashes; it provides some insulation (less effective than modern multipane glass, but much better than nothing), as well as physical protection (storm windows were often shatterproof acrylic plastic).
Temporary storm windows are a simple clear plastic sheet (plastic drop cloth, plastic tarp, etc., as long as it's clear), held in place by a strip of lath on each edge, which is stapled or brad nailed to the window frame. The clear plastic provides an airflow seal, some trapped air insulation, and physical protection (less so than acrylic sheet, but still much better than nothing), and is very inexpensive: they used to sell kits in hardware stores, but you can buy clear plastic sheet, lath, and brads cheaply at the big box home improvement stored. These are disposable; removing them in the spring destroys at least the plastic. They're cheap enough, however, that that isn't a big deal compared to the heating fuel savings.
Long term, you're best off if you can afford to have the windows replaced with proper multipane glass -- but temporary storm windows are a good, cheap, short term solution that worked well for many years before the current solution was available.