Recursive text search with grep and file patterns
My version of GNU Grep has a switch for this:
grep -R --include='*.txt' $Pattern
Described as follows:
--include=GLOBSearch only files whose base name matches GLOB (using wildcard matching as described under --exclude).
If you have a large number of files it would be useful to incorporate xargs into the command to avoid an 'Argument list too long' error.
find . -name '*.txt' -print | xargs grep <pattern>
you might be able to make use of your zsh's EXTENDED_GLOB option (docs)
grep <pattern> **/*.txt