Studs work really good on the ice that gets under a lot of trails and on the roads getting to the trails. They also help a lot when the rocks get all wet and slimy under the snow.
I've run chains in the snow when it wasn't too deep. They really helped but they dig. When it's only 2 feed deep, they really work great. When it's 6 feet deep, they only work if someone has made tracks that froze over hard then turned too slick to get any traction on.
I know a lot of guys make fun of snorkels but in your case, it sure would have been a nice addition.
If you aren't afraid of cutting the fenders, I think bigger tires would really help you. The difference between 35's which most brands only measure around 33" tall and a set of real 37's is a lot. That's 2" more under the diff and a huge difference in contact patch.
I'm working on some ideas for mine but my other half keeps telling me to fix the snowcat so we can wheel more and winch less...