First of all, while the refrigerator certainly did help, people used other means to cool food and keep food stored for long times. Ice coolers, where you would keep a block of ice in sawdust and have it replaced as it slowly thawed created cool spaces for the storage of food in Nordic countries' cities for a long time.

An earthen cellar would often hold a temperature of slightly above modern refrigerator temperature in both summer and winter. It was also dark, which prevented various root crops from spurting.

My grandfather kept his home-grown potatoes in his earthen cellar well into the 1990s since it offered a large dark, dry and cool storage space.

Mold and rot grows from "free" water food. You can either bind the water with sugar or salt, or dry the food to create less "free" water and prevent the food from spoiling. Salting meat and fish was extremely common and is recorded from the earliest times we have any records in Sweden.

Baking dry Swedish cripsbread allowed people to store bread for a long time. Drying peas and beans allowed them to be stored for a long time.

Norwegian dried cod was an important trade goods, not only because it offered a safe source of protein that could be transported and stored and returned to a decent state by boiling, but also because it was allowed during lent in medieval catholic Europe.

Once sugar became more commonplace in the latter half of the 1800s, preserving berries and fruit by making preservatives such as jam or lemonade with lots of sugar became common.

Controlled fermentation was also a way to preserve foods - foods that ferment become sour and bacteria causing mold and rot do not like a low pH. Cheese, sourmilk and sourcream became ways to preserve milk and cream (as did salted butter) and fermenting grain to beer or grape juice to wine allowed one to store such goods for a long, long time.

Goods extremely high in fat are also resistant to mold and rot. Pressing rapeseed or olives to oil allowed one to store that as well.

Flour is dry, and can be stored for a long time, so people would bake bread a few times a week as needed.

Peasoup, a traditional Swedish dish is made from onions (could be stored in the earth cellar), dried yellow peas (could be stored for a long time) and salted pork (could also last a long time).

TL;DR Salt, sugar, fermentation, drying, earth cellars.