Yes, a change in climate has a definite impact on our physical woes. I don't suffer from migraines but, I too live in the midwest, one day its dry and clear, then it snows, then it rains, crazy. I can only speak for myself, but with the moisture comes the pain. Arthritis, I would venture to guess that it would have the same cause and effect relationship, as well as barometric pressure.
The supplements that have brought positive effects for me include, Coq10, and cherries. For migraines the most research has been on butterbur, and feverfew. Butterbur being the most effective, but the most expensive.
Co q 10 increases blood flow to the heart, and brain. Calcium, and magnesium are relaxing to the body so therefor would relax the brain, and cherries have a natural pain killing compound. I found mine in with the other dried fruits, such as raisins, i keep them on hand, with nuts, and grab a handful whenever i need them.
You obviously cannot control the weather, but you can lessen the pain in a preventative way. I take coq10, cal/mag on daily basis, as well as krill oil. Not only does it curb inflamation, it also feeds the brain. You might consider taking on a regular basis as well. Extra magnesium at night, when you know that the weather change is coming, as prevention, and treatment.
I feel for you, pain is a very frustrating ailment. I always know when its going to rain or snow. Should of became a weather man, who knew?