You need to put the snippet into a folder with the name of the mode to use it in as follows:
snippets/org-mode/diary_template
Check out the documentation:
Organizing snippets > Basic structure:
.
|-- c-mode
| `-- printf
|-- java-mode
| `-- println
`-- text-mode
|-- email
`-- time
Expanding snippets > ... > Eligible snippets :
YASnippet does quite a bit of filtering to find out which snippets are eligible for expanding at the current cursor position.
In particular, the following things matter:
- Currently loaded snippets tables
These are loaded from a directory hierarchy in your file system. See Organizing Snippets. They are named after major modes like html-mode, ruby-mode, etc…
- Major mode of the current buffer
If the currrent major mode matches one of the loaded snippet tables, then all that table's snippets are considered for expansion. Use M-x describe-variable RET major-mode RET to find out which major mode you are in currently.
...