Hi christina.southa! Any property that is convertible to cash that a business owns is considered an asset. Since refrigerators have a useful life that is more than a year, you may include it under Furniture, Fixtures and Equipments as long as it is categorized to a Fixed Asset account type.
On the other hand Office Supplies are normally used for tracking Day-to-Day expenses (e.g. papers, pens,etc). However, Office and Classroom Furnitures such as desks, chairs or cabinets are also not considered as office supply items.
Hope this helps.
Thank You! =)