First of all, COBOL is a programming language, not a file format. If what you need is to export files produced by COBOL programs, you can use the same technique as if those files were produced by C, C++, Java, Perl, PL/I, Rexx, etc.
In general, you will have three different data sources: flat files, VSAM files, and a DBMS such as DB2 or IMS.
DMBSs have export utilities to copy the data into flat files. Keep in mind that data in DB2 will likely be normalized and thus you likely need the contents of related tables in order to make sense of the data.
VSAM files can be exported to flat files via the IDCAMS utility.
I would strongly suggest you get the files into a text format before transferring them to another box with a different code page. Trying to deal with mixed text (which must have its code page translated) and binary (which must not have its code page translated but which likely must be converted from big endian to little endian) is harder than doing the conversion up front.
The conversion can likely be done via the SORT utility on the mainframe. Mainframe SORT utilities tend to have extensive data manipulation functions. There are other mechanisms you could use (other utilities, custom code written in the language of your choice, purchased packages) but this is what we tend to do in these circumstances.
Once you have your flat files converted such that all data is text, you can transfer them to your Hadoop boxes via FTP or SFTP or FTPS.
Hope it will answer your question to an extent.