According to the Rules Compendium, can I charge through a square that would hamper my movement as long as it isn't difficult terrain?
Under "Initiating a Charge" (p. 27), it says:
If you don’t have line of sight to the opponent you want to charge at the start of your turn, you can’t charge that foe. To charge, you must move at least 10 feet (2 squares) and can move up to double your speed. You must be able to reach the closest space from which you can attack the designated opponent. This movement must occur before your attack. If any line from your starting space to the ending space passes through a square that blocks movement, is difficult terrain, or contains a creature (not a helpless one), you can’t charge. You can’t charge if the ending space is occupied or blocked. Since you move to charge, you can’t take a 5-foot step during the same turn. You provoke attacks of opportunity as normal for your movement.
It seems that squares that aren't difficult terrain, that only hamper movement but not block it are legal.
This would include Obstacles, Poor visibility (Any time you can’t see at least 60 feet in the prevailing conditions of visibility=Fog or Darkness?), and Squeezing.
Also some spells cause hampered movement that isn't difficult terrain.