I grew up here but spent 20 years around Boise (elevation 2700') granted Southern Idaho along the Snake River Plain is known as the Banana belt of the NW so we got much less snow than our MT neighbors. We lived in a town of 2500 people and the locals knew everyone's business. Didn't bother me though. I coached my kids in Tee-ball and baseball and that was a great way to connect with the locals that were in a similar stage of life. My wife was born in Boise but you may be surprised how many people never leave those small towns (Boise was the "Big City").
Helena (elevation 4000') being East of the Rockies gets that polar vortex occasionally in the winters which is pretty brutal. My wife and I honeymooned across Western MT back in 1998 and a lady in Kalispell (not Helena) recounted their population boom in years prior followed by a 1996 winter with 12' of snow. She said as soon as Spring came many of those new arrivals were on the first thing smoking out of town. Helena is more flat so you won't have that same issue Kalispell had due to the way weather interacts with the mountain topography.
Once Winter thaws you have what I call mud season until it dries out. Summers can find you with air quality issues from the wildfires.
Having always owned livestock, I had to use stock tank heaters and still broke ice with a sledge hammer. Not fun at 0 degrees as you can imagine. I really heard about it when I was out of town and the Mrs. had to do it.
You will get sick of winters the same way we get sick of summers here as others have mentioned, but seasons pass and maybe you snowmobile and ski so you can make the most of it.
Like Idaho, the timber companies have sold off large tracts of land we used to be able to hunt to folks that lock it up and will trespass you like those Texas Oilmen the W Bros.
You will have a leg up rolling into town with AZ plates on your rig instead of CA plates though.
Also, you will want 4wd or if you have a Fwd car you will want to put on studded snow tires seasonally and sometimes that will not be enough if you beat the plows on the road.
Also think about your proximity to family Parents, kids, grandkids, etc.
If you are the hearty type and the Mrs. promises not to get home sick, I would go for it. Just don't expect the cost of living to be lower.
I still have some snow shovels I can give you if you decide to go!
Good luck and have fun!