Since land mines (demonic bouncing betties, to be exact) are part of the TES universe, I was thinking that using explosions would be OK to see in Skyrim, mostly booby trapping stuff or laying out ambushes on the road.

Like a chest. You need to disarm the trap or it will explode, potentially killing you and completely destroying the chest and all its contents, which would fail a quest if you blow up the quest item inside (or make you look for another copy of the quest item, in perhaps a much more difficult location).

Doors could be rigged too, but when you blow up the door, that could be beneficial to you, as you can simply enter now. Or if it enters another cell, the door could cave in and become inaccessible for a few days (hardcoe: FOR EV UR, which would fail any quest you need to get in there for).

You could set up your own landmines, and based on your sneak skill, they are harder for the AI to spot and will do more damage. This would be great for ambushes and allow you to pair up with a bow and pwn everyone because the only way to you is through a mine field.