As to your reasoning for choosing Wyoming and your experiences once you got there... how your expectation were met or your disappointments, job situations, politics in your experience... for any and all of it you will find a very large audience and sincere audience.
The "welcoming" committee will be around 
Regards, Danl 
My husband had spent some time in Wyoming growing up, while his parents managed a ranch here. After a couple years with my husband being gone all the time with work, we wanted to find a place where he could be home and we could raise our children in the country. He first managed a farm for a few years until we found our place. There are tons of jobs here, if you are willing to work. It also does not take much to live here, if you are willing to work hard and can remain debt free. We get by on very little money, but we do alot of bartering and we try to produce as many of our needs as possible.
We moved here because we knew we were going to homeschool, were not going to vaccinate except for tetanus, we wanted to be able to teach our children to hunt, fish and shoot, and we wanted to be able to use common sense in building and running our lives rather than meet a bunch of foolish rules. We only go to the big city (Casper, population 55,000) once a month, and we enjoy the open spaces. Some of the children and I had asthma and after moving to the drier climate we have not needed meds in years. We have been disappointed at times, that Wyoming seems willing to give up it's freedom loving past. Smoking regulations, seat belt laws (even if it is just secondary), etc. Now one town is even trying to implement a daytime curfew. Even with those encroachments on liberty, Wyoming is still far better than any other state we have found.
As far as politics...that is the worst area for slippage in common sense, in my opinion. Even 10 years ago, most were rugged individualists and now there are many wanting a nanny state: national healthcare, state run daycare, etc. Casper, Jackson and Cheyenne should just move to Colorado.

The liberals are moving in and trying to change things, but the small towns are fighting it pretty well.
There is not a lot of diversity here. In the small town closest to us there were two black families. I only knew one of them, but they were the nicest people you could imagine. They said they had never been anything but welcomed, but they did move back to Ohio because their daughter was approaching dating age and they wanted her to marry within her race. There are some Mexicans, but not many, at least around here. All the farmers I know check green cards and will not hire illegals. Some people see the lack of diversity as a drawback, but I figure as long as other races are welcome (provided they are responsible) it really should not be an issue.
As a woman, I love it here! I wear dresses only and that may have something to do with it, but the men are respectful and helpful. Most of them will still offer to help you with your bags. I got a flat tire recently on a back road and all 7 cars that passed in the hour I waited for my husband stopped to offer assistance. When a person gets sick or injured, the surrounding community pitches in to help. It's just a friendly and caring state.
I know some people worry about the number of Mormons here, but I think it is wonderful! Their children, in general, are well behaved. When I had surgery the local church ward brought in meals for 7 days, and I did not know any of those women. We do share an interest in food storage and gardening, and we get together now and then for sewing days and such, and religion just has never been an issue. We have our beliefs and they have theirs.
I was raised in a rabid feminist/socialist household and my family can't stand it when they visit here. They think it's backwards and stuck in the dark ages. My sister said if one more cowboy opened a door for her, she'd scream.
The only things I had trouble adjusting to were the speed (people here talk and move slowly) and the stores. I was used to 24/7 access to stores and restaurants and you don't get that here. The only thing I still miss is good ethnic food, so I have learned to make my own.
The hardest thing about wanting to be self sufficient in Wyoming? Trying to grow food! In my opinion, if you are dependent on what you can grow you should have two years worth of food on hand. Even after ten years of gardening, our 2006 garden was wiped out by golfball sized hail and our 2007 garden was killed by June snowfall and September freezes. This year has been very cold and alot of things did not grow well outdoors, thankfully we have a greenhouse. We also grow wheat, oats, alfalfa, and corn, with other things thrown in now and then. We raise chickens, pigs, and beef. If you want to get rich, don't farm in Wyoming, but if you want to support your family it can be done comfortably.
I saw mentioned in another thread about registering to homeschool. Depending on your level of orneriness, it's not too bad. I do register, but not with the provided form. I give them our name and PO box number, the number of children we are homeschooling (but not their names or ages and the name/address of a publisher (we use many different publishers, but I just write in one and have never been questioned), I write in the letter that they do not have permission to put us in any database or share our information with any person or agency.
We have a handicapped child, who is under legal school age. We explained that we would not sign up for early intervention because of the laws (they can turn you in to DFS if you try to quit) and they were very understanding - to the point of saying they disagreed with the law and it would never be an issue with them, but they could not guarantee it would be that way if they changed personnel. When we declined services, the OT, PT, and SLP all spent hours with us helping us develop our own therapy programs. Our son is steadily progressing, and the Dr. (who was very against us doing it but is fine with us not vaccinating and such) says our son is doing better at home, anyway, with daily therapy rather than the twice a week he would get through the system. I share this not to toot our own horns, but to show that even those who work for the system disagree with it here and will help you stay out of it.
I can't think of anything else that someone might want to know, but I don't mind answering questions.