Is it possible to upgrade mongodb cluster without upgrading arbiters? Is it possible to have running real nodes with version 2.4 and arbiter nodes with 2.0 or 1.8 in the replica set?

Upgrade guides for version 2.2 and 2.4, did not tell anything about upgrading arbiters.
The general recommendation is to have all members of a cluster or replica set running the same version, inclusing arbiters.  Hence, generally you should upgrade arbiters when you upgrade everything else.  In fact I would say to upgrade them first since if you have things configured correctly there will be no interruption in terms of operations from an arbiter upgrade (barring an outage elsewhere while you work).  

They will probably work just fine with mixed versions, but since you would be then running in an untested (for long term use) configuration, if you run into any issues at all the first advice is going to be: upgrade.