Choosing secondhand keeps bulky appliances out of landfills and reduces the environmental impact associated with manufacturing new units.
Most private sales are "as-is". If the fridge dies a week after you buy it, you have no recourse.
Older refrigerators (those over 10 years old) can consume up to 40% more energy than modern, Energy Star-rated models. What you save upfront might slowly leak back out through your monthly utility bills.