Since you don't plan to leave the pavement too often, I wouldn't be too concerned about an all-terrain tire. They are definitely not a winter tire. They are not really even good off-road tires and they will not be of any benefit to you in the rest of the year. Thier only purpose, IMHO, is to make your truck look like a truck.
A good winter tire will stop on ice better by very surprising multiples and the difference in moderate snow is similarly dramatic. Some are designed more for ice and others more for clearing snow from the treads. You generally trade a bit one way for the other.
You are correct in that most winter tires are not designed for silly amounts of snow and despite advertisements of them tunneling through the alps, you won't hear any true verbal claims about being able to master real deep snow. However, they will still be an huge improvement over all-seasons or all-terrain.
Want to really play in the serious snow? You need an expensive off-road tire that won't self destruct or fly off your wheel when you purposely deflate them to 10-12 PSI or less. Because, seriously, that's what you need to float over the snow and/or spread your weight over enough tire surface that it gets really hard to get stuck. Even then, once you get high centered (the weight of your vehicle is sitting on the snow by it's belly instead of the tires) you're screwed. Clearance beats all but the worst tires, every time, in snow.
My last thought,
The FJ is a pretty heavy rig. Keep in mind that whatever type of tires you invest in, they will need to be a light truck tire at minimum.
