If you have washing facilities that you can use then I would take the cloth - if you have enough nappies, you may only need to do one wash and then bring back a load of dirties. We went away for 2 weeks and I used the washing machine in the holiday cottage once and a launderette at the caravan park twice. It was lovely and sunny so could hang them out to dry. I have a huge swaddlebees wetbag which holds a good 3-4 days of nappies without having to worry about smells. And I took gDiapers which are like AI2s so could just use a few outers and lots of prefolds and terry squares as inserts which open out flat to dry quickly.
However, if you are not going to use a machine, I would not bother - it really is hard work hand washing them and then you can't wring them out like a washing machine spin so getting them dry in the depths of winter would take an age. If you want to enjoy your time away, either use the washing machine or take sposies