Housing will be your biggest expense. I don't know if you have found a place to live yet, but I would go through rental agencies/property management agencies (I don't know if too many real estate agencies do rentals here; Oxford does both, but otherwise, I haven't seen too many real estate agents in the rental business). I would be very wary of Craigslist because many scams show up on there. People will swipe legitimate postings and repost them in the hopes that someone will send them a deposit for a property they don't actually have. Elite and Oxford are legitimate companies. So are some smaller ones, like IMM (Investors Management and Marketing) and others. Like others said, rentals are mostly apartments; houses are mostly owned. Rental houses for families are harder to come by, and the more affordable ones tend to be very elderly houses that often have only one bathroom and aren't necessarily in great shape. I know they've been building more housing since we first moved here, though, and hopefully that means more family rental housing than there used to be.
Food is higher here than in other places, too. I think that if you are very frugal, you can live on 45K. It will be tight because of housing, though. There will be some large startup costs for you, though (like filling out winter clothing needs). Become well acquainted with thrift stores (you can often find things like used ice skates at thrift stores, for example), watch sales at places like Scheels carefully (they carry high end sporting goods/winter clothes/athletic shoes, etc., with high end prices, BUT--they also have good sales). It'll be tight, but your kids are also small, so they probably won't be spending money like teenagers.
The schools themselves are good. GF is a town where all of the schools are pretty much equal in comparison to each other--so you don't have to worry about living on the wrong street and getting stuck in a "bad" school. We lived here for a couple years, then went to Alabama for a year, and just last week, we moved back to Grand Forks. I cannot even tell you how much easier it was to do school transfers and all of the moving paperwork here in ND than it was in Alabama! There is an air force base nearby, so they are aware of the fact that people live in other places, too.
I know you're worried about winter (you will be cold the first winter, but you will adapt eventually!), but I have to say that summers can be nice here. There are hot, sticky days (especially if you are used to a dry climate), but there are a lot of very pleasant days, too. There are several outdoor pools in town and there's a long bike trail along the river. In winter, you can join Choice Fitness, which has an indoor track, gym, and pool. Kids play outside year round, bundling up on days around 0 Fahrenheit to play hockey outside. Lincoln Park (and maybe others? I don't know) does free skate and cross country ski rentals in the winter--they groom trails and also flood over and polish a section of the park for skating.
Anyway, you're definitely in for an adventure. Welcome, and good luck!
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