It's kinda late to post here I know, but I just saw this. I restore log/cedar homes for a living and have your answer on the mold issue. Linseed oil has sugars in it and mold loves sugar. A solution would be to mix a borate with your oil, downside is that borates have insecticides in them.
This is now my second year and what I've done with my hives is put on a good quality log home stain on most of my hives, left a few alone, and had a few in white. The results of the ones left alone are that they are covered in black mold. The ones I stained still look great. I stained the lids and they tended not to warp and still look good. I chose to use ArmstrongClark stain, It's a great no brainer stain that has great track record. When it needs a recoat, you just wash the hives down in a little bleach water and restain. You can use a pump up sprayer to stain them, no brushing. You can Stack 'em a dozen high, use a pump up to apply the bleach, let it sit for about 10 minutes, rinse 'em off, come back in about an hour and spray the stain on and you're done. *from my experience the stain will last 3 years and if using a telescopic cover and high off the ground, it could last up to 5 years.
**I would warn that I'm still experimenting with this because stain has insecticides in it and could kill the bees if any got on the inside of the hive. I also let the hives defume for a couple of weeks before using them. I also didn't stack all stained boxes on one hive, I mixed them. This year I will experiment further, but so far they're alive and the wood looks fantastic. It would probably be even more beneficial to let them air out all winter, the fumes stick around for about 6 months.