When I use logging modules (eg winston) and write to custom log files (rotating names based on date), how can I download those dynamically generated files from openshift?
You could store the logs in the $OPENSHIFT_DATA_DIR (~/app-root/data) on your gear, and then just rsync them to your local machine:
rsync -avzh ssh <gearid>@<appname>-<domain>.rhcloud.com:~/app-root/data/ /path/to/dir