I don't know the housing market in BCS, but my house is in Houston. If you want to live anywhere close to work in Houston, you're looking at $350k+ (heck, most of the burbs are that price as well + higher taxes + ridiculous HOA). You can find a nice place in Billings for $350k. I'm currently renting and pay $1,850 for a 5 year old, 4 BR, 3 Bath, 2 garage, 2,200 sqft townhome in a nice neighborhood. I paid $1,600 for similar in the suburbs of KC, KS and my house in Houston (inner loop) rents for $2,700, just a little perspective.
As far as other cost of living things, gas is more expensive (2.30 right now), utilities are higher, there is a state income tax, and travel is more expensive (although I've found good deals) and takes longer since there are no direct flights anywhere. Compared to Houston though, it isn't all that much higher since Houston does have a high property tax (on bloated house values) and a high sales tax. Vehicle registration is high in MT as well.
Billings is the perfect big little town in my opinion. Small town feel, but access to everything you need without trying too hard. As far as crime and drugs, sadly, that's everywhere. I don't think Billings is any better or worse on that front. Your kids are going to have access to meth and pot and coke in BCS just as easily as Billings.
There is less access to 'things''ethnic' restaurants, grocery stores aren't stocked the same as a Houston store (artisan foods, etc), Amazon prime isn't really 2 day shipping a lot of times.stuff like that. Nothing you can't live without, but if you're into stuff like that, it's an adjustment (doesn't sound like you are though). There still is plenty of stuff here though. Hell, we have 3 Walmarts within 20 minutes!
There are plenty of good restaurants, shopping, and other things to do like shows, movies, concerts, arts, plays, parks, symphony, etc.
Winter isn't bad, I've lived in worse. Yes it's cold, it's winter. Texans a lot of times don't grasp the whole 'seasons' thing. Winter cold, summer hot, gorgeous transition in between. I think we got to -40 wind chills in Billings this winter and have had at least a foot of snow on the ground for 2 months. But if you dress for it and prepare for it, it's no big deal.
As far as schools, I'm not real sure as we don't have school aged children yet. They seem to be okay, not great, but compared to the schools my kids would go to in Katy (probably move there once we move back to TX), they're probably not good. That's asking for a lot though, to be compared to Katy. I went to a crappy school in a crappy state (New Mexico) and turned out okay, as did most of my classmates who applied themselves. If you're kids have the smarts and work ethic to be a dr, lawyer, engineer, etc, they'll get there, regardless of where their primary schools fell on the rating chart. I do know that I'd feel better about putting my kids in school in Billings vs Houston ISD.
If you're outdoorsy, you'll love it. Excellent access to hunting, fishing, camping, hiking, off-roading, shooting, skiing, snowmobiling, etc. Access to national parks like Glacier, Yellowstone, and Tetons. We spent almost every weekend in the summer in the mountains a little over an hour away.
Sorry for the rambling nature of this post. I'll add more as I think of them. If given a choice, I'd stay here forever (or at least for a very long time anyway).
Here's a thread I started a couple of years ago about the same topic.
https://texags.com/forums/55/topics/2534076