if you are talking about red mite yes they can live without chickens and they can live for up to eight or nine months without feeding. The cold weather does not kill them it just slows them down. If you introduce chickens again and you still have red mite they would go on a feeding frenzy as they had not eaten for so long and cause the hens a lot of problems
It sounds to me from the link posted earlier that they only live on the bird unlike mites that can live off the host for some time. So if the chickens that had lice are gone so are the lice (from what it sounds like).