How to query readonly replica in Always On cluster
After some help and hints (especially thanks to Andriy M) I've managed to understand what I actually want and how to do it. This article from Microsoft helped as well: https://technet.microsoft.com/en-us/library/hh403414.aspx

First I had to create a read only listener. And then at the other server add linked server like this (borrowed from: https://stackoverflow.com/a/19585304):


USE [master]
GO
EXEC master.dbo.sp_addlinkedserver
    @server     = N'cluster-readonly', -- just a name
    @srvproduct = N'SQL', -- anything except 'SQL Server'
    @provider   = N'SQLNCLI11',
    @datasrc    = N'ClusterListener', -- name of the readonly listener
    @provstr    = N'ApplicationIntent=ReadOnly',
    @catalog    = N'AnyActualDataBase' -- system database like 'master' is no good
GO


How do I check, where am I:


SELECT * FROM OPENQUERY([cluster-readonly], 'SELECT @@SERVERNAME')


Here's some trick - if I don't specify @catalog, then connection will be to the PRIMARY node for some reasons.