Ozone will kill it. I have a small ozone generator that I use to keep the air free of mold and other toxins.

I have not heard of Ozone killing mold before. Would like to here back if you try it and it works!
Mold is in our environment everywhere and impossible to eliminate completely. Most would just approach as attempting to control the growth as much as possible. Keeping the relative humidity below 55% is key to controlling the growth when temperatures are in the 50-70 degree range. Then trying to reduce surface moisture or condensation. I do use a humidifier for this as well as ventilation, on sunny days for a short time, as to not lose all my heat. If it were me I would wash down all the wood surfaces with a bleach water solution and a sponge. After completely drying then seal the wood. I'm not sure if you are going to be able to get the wood dry enough or warm enough to accomplish that this time of year, but if and when those things come together I would get it done. I have my entire greenhouse trimmed in wood and do not have a mold problem with the wood. When built I sealed the paneling and railing with BEHR Premium Transparent Weather Proofer Wood Finish and have not have a problem to this point. This will be my forth winter. I did have a big problem with mildew on all the soils and found that scoria an inch deep solved the problem. I have a dirt floor due to the citrus trees planted in my greenhouse.
Pics attached
Hope this was helpful.

Didn't know about the ozone generator - I have one and will use it if the situation arises!
many thanks
Lori

Another option is H2O2 spray (hydrogen peroxide). It is sold commercially but a commercial GH grower once told me that they use drug store 3% H2O2 diluted properly. (It's been a while since I've used it, but recall it is 1:9 for the 3% to make a spray)

It is not safe on all plants, but many can tolerate it. However should be fine for structure.

Physan 20