The last 32 bit version, which was available for Windows 7 (I think with service pack installed) and later, was Picard 1.4.2. We removed it from the download page after it stopped working a year ago due to outdated Open SSL, see [Solved] Picard cannot fetch data from Musicbrainz.org . As mentioned in this thread there are still ways to make it run, but it is no longer officially supported.
The last 64 bit version is at this moment the official version 2.5.6. It runs also on Windows 7 (with service pack and fully patched) or later. For now I see no need to change this requirement. The next releases will for sure have the same minimum requirement, although I cannot say for sure how long Windows 7 support will be feasible.
Should we need to drop Windows 7 support in a future release for some reason we can keep the then latest version still supporting Windows 7 on the download page.