You would hang them indoors. Even rather grand homes would have to do this - and the grander they were, the more there would be. Where? Well, the dining room or the ballroom. perhaps. One or more chandelier hoists, probably two fireplaces, more than enough room to lay down an oilcloth.

Homes built before central heat and air tended to have very high ceilings, even if they had a small floorplan. It was possible to set up natural convection patterns that way. (The Winchester Mystery house is a less mysterious if you realize that some of it's features have to do with heating and cooling. )

EDIT: Holy moly, reddit, how strange is this? Over in /r/whatisthisthing we see another solution for indoor drying.

Very cold air is also very low in humidity. So when hanging wet laundry outside, the moisture would still evaporate, especially if it was windy. My mother would beat the frozen laundry to knock off the ice and expose more of the fabric to evaporation. The shortcoming of this strategy was typically the limited sunlight, rather than the temperature.

Most homes before electricity and home heating oil would burn coal or wood 24/7 in a stove in the kitchen. The burner would not only be used to cook/roast/bake food, but would heat water and warm the house. Hanging laundry in the warmer kitchen because the stove was there was common practice.

Even though electricity was deployed thought the U.S. during the first half of the 20th century, it was not often used for direct heating due to its high cost. Its use in home heating was, and still largely is, limited to pilot light ignition and circulatory fan power.

(Born in northern Minnesota in the 1950s)

Edit: Yes, I just slam my fists down on the keyboard and backspace over the characters I don't want.