How about you hang your clothes indoors when it's raining inside? I've been doing that for years in a rainy country in a tiny studio apartment. No issues.
Dehumidifiers are pretty affordable and warms up your room a little. Still doesn’t solve the fact you need to ventilate your home. If you can - isolate your drying to a non living space.
The water that was in your clothes and evaporated over 12 hours at night naturally is the same water that evaporates in 1 hour in the powered dryer.
If you have working ventillation you're fine either way. If not - you're not. In fact I'd expect worse problems if you evaporate that same water quicker, because there's less time for it to escape outside.
Usually dryers are connected to dedicated ventilation out of the house, so the humidity doesn't transfer into your room directly. Otherwise, the laundry room would be a sauna.
Dryers typically are vented immediately outside via a dedicated tube and vent. That means that the air in the rest of the house never sees the moisture at all, so your whole-house ventilation system or dehumidifier doesn't need to work as hard.
Some driers, especially in Europe, condense the water in to a tank that you empty manually in to a sink. This is useful if you don't have an easy way to vent it and also shows just how much water is coming out of your clothes (multiple liters per load, sometimes!)
Still dependent on the overall climate. It's not necessarily about how much it rains, but how humid the air is. When I was in Virginia, it rained a lot, but the air clears up fairly quickly after rain.
In contrast, my grandmother lives in a village with such incredible rainy seasons, that this has been a pain point as perpetual as the rain itself. For a few months in summer, the air is so humid that even unused clothes have trouble stay dry. Condensation appears on the wall, and nothing ever dries, no matter where you hang them; indoors, outdoors, doesn't make a difference. Sometimes, they have no dry clothes for weeks during summer.
You put your clothes there, and the next day they are dry.
Other common solution is collapsible drying racks on your balcony: https://images.morele.net/i256/12998234_0_i256.jpg
Or just clothes lines (but usually people have some backup in case it rains).
I've never seen people use powered dryers for clothes. And we get our share of rain, and in the winter it gets to -20C sometimes.