I live in a small 12-ft yurt in Austin where humidity can be a problem, especially in the summer. Other people with more cold weather experience should chime in. There are several things that help. One thing is that there has to be a way to get moist air out of the yurt even when you want it really well sealed, like in the coldest part of winter. Most
systems remove moisture from the air and insulation, which is helpful. But I feel that all yurts should be designed to do some controlled outside air exchange even when fully buttoned up. I love catalyzed propane heaters, but they create water vapor as a by-product, and they already require a bit of venting to be safe. Many people aren't aware of the water production and are surprised by the humidity.
My insulation is made of cast-off comforters and sleeping bags. I take them down seasonally and wash them to prevent them from getting too dirty. My resident gecko and anoles get very upset when I do this. Allergies in general are also terrible in Austin, so I just got a small Holmes HEPA air filter, which are available consistently at thrift stores super cheap. The real problem with mold getting worse and effecting health is when the spores spread, which usually happens when transitioning from moist to dry. If you filter the spores out of the air regularly, it never has a chance to get worse. I've already noticed an air quality improvement from when I installed the filter.
I'm going to be adding a layer of Reflectrix bubble wrap insulation to at least the ceiling this summer, but it's supposed to help in winter too. It's pretty mold-proof.
One thing I've found really helps with any allergy problem is lower-carb dieting. When I've been very strict on it for months, things that previously would have sent me into flu-level misery barely effect me. It lowers systemic inflammation, so the extra one gets from various allergens are less likely to push one over the edge.
Insulating the floor well really helps. I have only 3/4" foam insulation, and my floor gets pretty cold if I don't heat it constantly in the winter. I also have cork flooring, which is looks and feels great and helps with insulation. I keep my little electric space heater on the floor and pointed toward the center from the side. Once the floor is warmed up, I can maintain 65 o F inside when it's in the 20s outside with one little 1500 watt space heater. But if I leave for a few days and let the floor get cold, it takes a whole day to re-warm. If I lived in a cold climate, I would take the time to install a basic heated floor. I get the most even heating in the yurt when I start from the bottom. Otherwise I get the floor at 55 o F, the middle at 65 o F, and up by the plugged roof ring at 75 o F.
The main point is that moisture will build in a sealed yurt until it is a problem unless is removed somehow.