If you use any of Google's web products, you should be familiar with searching by dates using keys like...
- date:
- between:
- before:
- after:
Yes, Picasa naturally organizes photos in date named folders. However, this convenience is lost when importing instant uploads from Google+, which just drops a pile of photos/videos into one "Instant Uploads" folder.
What the Picasa search bar does do is index all text fields/tags in your photos. If EXIF data is saved with your photos, there is a field called "Camera Date" which holds the date (according to the camera) that the photo was taken. This field is formatted as:
yyyy:mm:dd hh:mm:ss
(where hours are in 24-hr format)
So, if you want to search for June 2012 photos, type:
2012:06
into the search bar. So, while this works to grab photos from a specific month, there still isn't a way to find photos from a specific date range. Hopefully, this will be a new feature in an upcoming release.