My summary of what W. Steinitz (Deutsche Volkslieder demokratischen Charakters aus sechs Jahrhunderten) writes about this song (with some additions from E. Klusen, Deutsche Lieder):

The line 'Die Gedanken sind frei' (or similar formulations) is very old and goes back to at least the 13th century. This particular song, however, has first been found on broadsides 'between 1780 and 1800' in Southern Germany. The lyrics vary, of course. The tune is said to be an Austrian folktune.
The song has probably been forbidden in the Vormaerz-time (the decades before the 1848 revolution) and the verse 'Ich liebe den Wein' is a later addition from that time, probably to evade the censorship. In many version, this is the first verse, and since most German folksongs are know by the first line, any censor who scans the first lines will be duped by 'I love the wine and the girls' and let the song pass.

Other verses from several sources cited in Steinitz are:

Beleget den Fuß mit Banden und Ketten,
dass von Verdruss er sich nicht kann retten,
so wirken die Sinnen, die dennoch durchdringen.
Es bleibet dabei: Die Gedanken sind frei.

Wird gleich dem Gesicht das Sehen versaget,
so werd ich doch nicht von Sorgen geplaget.
Ich kann ja gedenken, was soll ich mich kränken?
Es bleibet dabei: Die Gedanken sind frei.

I have no factual basis for the following speculation: C.F.D. Schubart was a poet, writer and editor and political prisoner in Hohenasperg prison from 1777 to 1787, the first 377 days in complete isolation. I fancy the thought he was the author of the song but didn't want it to be known for obvious reasons. The timing fits the speculation as well as the style and the location of the first occurence of the broadsides.

Wolfgang