Visit the site in January for a complete picture of what it is like 6-7 months per year.
Check out water well depth and past permits in the area from the state engineers office.
There is a reason that windsurfing is popular on Lake Hattie.  Wind is a 365 day/year event.
High speed internet out there would probably need to come from a satellite.  Not sure anymore, been a while since I lived in Laramie.
Did I mention visit in January?

This is a beautiful corner of the state, but it is brutal in the winter.

I didn't google to see exactly where it is but I'm guessing in the SE part of the state, more than likely near Laramie.
If you don't like winter and wind it's not for you.
They run TV commercials here for those type of 40 acre lots and the one I see most often I drive by the old ranch on my way to the Snowies and you couldn't pay me to live there year round.
There's a reason not many people live in WY and most of those that move there don't stay.

ETA: as far as good mountain living out west.....it's not going to be cheap for desirable land and/or location and 40 acres isn't much out there, need to add a 0 to that number

10 day forecast for Centennial which is pretty close to that area

If I could find a way to make a decent living I would live in the Spearfish area of South Dakota.
If you truly can work remotely that opens up a ton of options, lots of places in Utah, northern New Mexico or Arizona.

The problem with WY is the southern and NE part of the state are pretty flat which means wind, the real mountains are in the NW part of the state which means you're farther north and more than likely higher elevation which means harsher weather.
Go to this thread and look at the pictures and that will give you an idea of what the majority of the state looks like, wide open with no trees and some interesting terrain. The NW part of the state IMHO is one of the most beautiful parts of the lower 48.

TOPO map of WY

Most of Wyoming is similar except the Northwest and North-central.  Land is expensive up here.  Probably the warmest place in Wyoming is Torrington, and that is because it is far-west Nebraska.  Mountains aren't really close as it is mostly grassland.  Since you have school age kids, if I were you I would look at the area of Grand Junction, Colorado.  It is dessert but a short drive to the east and you're in the mountains.  A drive to the West and you are in the dessert with slick rock (think Moab, UT) where your SO with her Jeep will have tons of fun.  Grand Junction is west slope and the politics wouldn't be as far left as the front range around Denver.

A very old school tag.

Sorry, I did not notice this thread until today.

Take everything I say with a grain of salt, because it reflects my priorities (which may not match yours).  I live just outside of Cheyenne (the state capitol) and the only high speed internet I can get at my house is satellite.

If you do not like winter or wind, elevation is not your friend.  Laramie is at 7200 ft above sea level.  Winters there are long and hard and the wind pretty much blows all day long 365 days a year.

OK, where would I live if I did not need to leave my house to work (and I was young enough not to expect to need immediate quality medical care at some point in my near future)?  I like trees & mountains and I (for the most part) hate people, wind & winter.  Elevation is my enemy.

The lowest point in the state is 3125 ft above sea level where the Belle Fourche River crosses the Wyoming/South Dakota state line (northeast corner of the state).  The Black Hills (Sundance, Hulett, Alva, Aladdin, Devils Tower, etc.) are absolutely beautiful and have as close to four seasons as you are going to get in Wyoming.  Drive to Rapid City SD for major medical.

The Sheridan (3735 ft) to Buffalo (4645 ft) area on the east side of the Big Horn mountains (north center of the state) is another good location with reasonable (for Wyoming) weather, mountains & trees.  Drive to Billings MT for major medical.

The Lander (5387 ft) - Riverton (4956 ft) area (center of the state) is beautiful and the wind only blows about 50% of the time.  The major downside (for me) of this area is that it sits on the edge of the Wind River Indian Reservation.  I have no idea where they fly you to if you need major medical treatment.

The Star Valley area has very little wind (for Wyoming), but longer winters due to being just south of Yellowstone & Jackson.  Afton (6134 ft) south to Cokeville (6191 ft) is a beautiful area, I have always wanted to live there.  It still might be the most affordable of the nice areas in Wyoming.  I believe you have to drive to Pocatello ID for major medical.

The more desirable the location, the more you will have to pay per acre, because the tourist (millionaires) have already found it and driven up the prices.

If you don’t have a million dollars to spend on 100 acres of ground and don’t need to leave your house (drive to town) but once a week, someplace like Shell, Hyattville or Ten Sleep (west edge of Big Horn mountains, north central) might be exactly what you are looking for.

Good luck on your search for a new home.

Snowed an inch overnight and was 13 this morning with a nasty wind.  Never got to freezing.

Powell area.  I suggest Utah.  That's where the GF and I will spend time in the winters when I retire.

If you can tolerate winters here, and want 'views' and 'solitude', look at Big Horn County (western side of the Big Horn Mountains and 1.5-2 hours south of Billings). I would guess that the best bang for you buck on property that your looking for would be there. Of course if you move there you'll eventually become a 9er, and you gotta ask yourself if you really have the  potential to be a 9er. The rest of us will laugh at you and make fun of your driving, but you won't care......because you'll be a 9er.

Okay, I'll bite - what's a 9er?

A 9er is a state of being, a state of mind, a state of alternative reality, a state of uniqueness, a state of fierce independence.......

Ok, it's really just the number on the license plates for Big Horn County "9", but the folks there are just a little off....but we love them for it.

Joking aside, do look at property there if you want value and views. Just saw a 37 acre lot for sale near Deaver for 40K (asking). Some friends just built a home near there, spent about 300k for a huge home (4000sqft) with picture windows facing the Big Horn and Pryor mountains, absolutely stunning views. 30 minute drive from there will put you on top the Big Horns.

That development is out off Snowy Range Road heading out of Laramie towards the Snowy Range Mountains. Yes, you get pretty views of the mountains off in the distance, but you are on the Laramie flats (prairie land) with no trees. It does get windy out that way. And like today, if you had traveled to say Cheyenne for something earlier in the day, you'd be stuck there due to road closures. I'm stuck over here in Rawlins hanging out at the Holiday Inn LOL. Roads were decent this morning, but turned to crap on the summit between Laramie and Cheyenne. Most times it's not the amount of snow that closes roads, it's the combination of snow and wind. Commercial vehicles (like i drive out of Cheyenne) and automobiles start sliding into each other and into ditches, they shut them down.

I wonder if New Mexico wouldn't be more your speed. The weather is much more mild, though the state has severe economic problems that I partially attribute to the collapse of the uranium market. The high desert out there is quite nice, and the mountains are gorgeous. I'm partial to the Kelly/Magdalena area myself.

Here is a good blog of living in WY.

https://www.theprairiehomestead.com/2015/12/homesteading-in-wyoming.html