When skiing in the backcountry (or even in the trees at resorts), what can be done to minimize the risk of getting trapped in a tree well?
Don't ski alone. If you do fall in one of these, it will be much more difficult to get out on your own than if you have some help.
Obviously, being aware of what these traps look like can help you avoid them. When you do see one, take the necessary precautions and investigate it. How far from the trunk do you need to be to be safe? I already purposefully jumped into one, knowing that I had many friends and plenty of rope to help me get out. It's just good to know what you're up against, really.
If you do fall, try to use your skis and batons to break the fall. They are long and using them horizontally is a good way of avoiding sinking in the snow.
If you do fall in, taking your skis off can help you maneuver you feet, but keep your skis handy as they can help create a solid support on which to push or pull yourself up.
Whatever happens, don't panic and think of the consequences of each move before you do it. For example, don't just put a foot on the snow and push, you might break throught and worsen your condition.