There's plenty of places down south that get lots of snow, most are around the Great Lakes, Northern Plain States and Rocky Mountains. My experiences with snow and Texas are that when it snows in Texas we get to see the news anchor on CNN with cars and trucks in the background sliding into each other on the highway
I couldn't say for sure on the snow tires, but they are probably in the $150/each range for the FJ. Most people have two complete sets of tires, winter and summer. You should easily get 4 seasons out of a set of studded snow tires. They will be cheaper in and around Anchorage than any other town, so If you find that your are going to be stationed in SE Alaska, get them in Washington if possible. Another common sight is cheap steel rims for winter tires so you don't have to pay $50 every 6months to get your tires re-mounted, so if you have a place to get some inexpensive steel rims you might want to think about that as well.
Surprisingly, the cost of living up here isn't as far off as you would think. It's not cheap up here, but there are more expensive places to live. None better though if you ask me
