We saw in the Administration Console that we have many many many Workflows which are running since 2011.
Is it possible to cancel all Workflows that are in the Running/Errored state befor (for example) 1.1.2014?
You can use the NWAdmin.exe tool or you can do this via the Workflow Purge option available to Site Collection Admins. Either gives you that option.
Great post reference Fernando.
You go to Site Settings->Nintex Administration->Purge Workflow Data. Here you can create a custom filter like State is Error or State is Cancelled and you can specifiy Last Activity Before and then a date.