I've never pruned peppers. As with jmusser, if they survive winter in a pot, then I plant them out after the last frost (this is Texas so it is fairly warm by the time frosts are guaranteed gone).
If you are keeping it in a pot (seems popular in the UK, although you should be able to plant them out in a similar manner as tomatoes), then I would remove the dead plant, and probably the nearly dead green stalk; then choose a larger pot. I find pots restrict the size of a pepper plant (those in beds grow much bigger).
Otherwise I think it looks healthy. At this stage, better than any 'edible' pepper plant that I've managed to overwinter! (I currently have some ornamentals doing well, but they are tiny plants with tiny fruit)