I haven't played too much of the game, but I am aware status cards can be removed by applying other cards such as traits and over cards with a duration (which affect characters directly). Are there cards which do the same? I can imagine a version of Charge, for instance, which has a conditional effect if a character is encumbered (a version which does not do damage or decreases the movement that card gives). It could remove one card with a hindering effect. Or a trait card (say, a dwarven racial) which makes the character ignore/remove one card with a hindering effect played to affect that character after the trait became active for a certain duration. I'm making this because encumbrance effects can be so debilitating I think they pretty much need to be taken into account.
I believe Purge and Holy Presence are the other most direct examples. Arrogant Armor is a rather rare card. And then there are the recent Elf Skill changes listed here: http://www.cardhunter.com/forum/threads/upcoming-balance-changes-7-august-2013.2984
Best solution is to have plenty of team moves. That saves a multitude of sins. They encumber you, they lava pit you, they have no cards left and you charge up with two warriors and batter them to death!