I’ve had these for years, and in places not considered “cold” (Tucson, AZ, and Bay Area, CA). My understanding of what causes them matches what @IsaacBB said: fast changes in temperature. Basically, when you’re done with a ride and your toes are freezing, don’t jump into a hot shower immediately. Try to let them warm up gradually. That’s easier said than done, and I’m not very good at it. (I had one podiatrist also say not to walk on cold tile.) I will say that waiting for them to warm up is definitely the right thing to do–my feet got pretty freezing after my race in the rain on Sunday, and I forgot to bring fresh socks. In addition to the post-race chit-chat, I had an hour’s drive home. It took forever for the toes on my right foot, in particular, to finally warm up, but I didn’t get chilblains!
For training outside, I wear wool socks and booties, and use those chemical heaters when I’m riding in the cold, but my toes still end up getting cold. My chilblains don’t show up right away–usually it takes a day or two for full impact. Maybe now that I know for sure that waiting is the best answer, I’ll try to wait a little longer for things to warm up naturally. If you’re getting these while riding inside, I’d try the chemical heaters. My recommendation is to put them on top of your feet (on top of the socks). You have better circulation on the tops, and the skin is thinner.