Arjen,
the German Wikipedia has an article on Umlauts that describes the possible evolution of ae > æ > a with superscript e written in some kind of German script [see Sütterlin] > ä.
Of course, there may be other explanations to the same phenomenon, e.g. the e getting smaller and smaller in medieval script or the like.
These Umlauts were quite common in Fraktur types of all origins, also up to the 1930s (though not necessarily in all blackletter types).
My example is from J.J. David, Gesammelte Werke, München und Leipzig R. Piper u. Co., 1908:

Paul Antonio
www.PaulAntonioScribe.com

There might be another reason for the little 'e' shaped umlautt! In Seutterlinschrift the shape over the 'u' to distinguish it from the 'n' and 'm' (lower case) is a harken and it is like a slightly exaggerated comma.

In looking at the little 'e' shape it seems to me that it might have originated in the handwritten form as most of these things are.

A little comma is interesting in that a daub with the nib of the quill would create a dolop of ink from which to pull the tail of the comma but if the nib was cut for square pen scripts then the ink might not readily flow and so would need a lead-in stroke/serif to initiate the flow of ink. If you start with the internal cross bar of the 'e' this then up and over, around and down would quite happily create an 'e-like' shape.

The existence of 2 'horns' on this like of 'e' could then lead to some interchange with 2 dots as the horns would look like 2 dots! But this mainly in the formal Fraktur and not the more rounded Schwabacher!

What do you think?

Paul

Paul,
while it seems possible from a graphic/chirographic point of view, I don’t think that your idea is of any relevance due to the linguistic necessities of the German language.
In Suetterlin (and of course, also in earlier instances of "German" Kurrent handwriting systems – your argument would also be historically out of place as Suetterlin was a creation of the 20th century whereas the first printed Fraktur types with this kind of e-shaped umlaut may date from as early as the 15th century) any u is written with this small mark, and any umlaut is written with two small dots or strokes. There is no connection between the two strokes, and if there were one because of casual writing, any reader would easily discern whether ü or u were denoted depending on vocabulary and therefore context of the letter. The same would apply if one wrote a Suetterlin u with a e-shaped u-mark as you suggest.
To sum up: My main concern with your idea is that an u is not an ü.

if i'm not mistaken, the two-dot umlaut derives from the script form of the german e. see the English Language Wikipedia for details.

Paul, I presume you refer to this part:
Originally, phonological umlaut was denoted in written German by adding an e to the affected vowel, either after the vowel or, in small form, above it. (In medieval German manuscripts, other digraphs could also be written using superscripts: in bluome ("flower"), for example, the <o> was frequently placed above the <u>.) In blackletter handwriting as used in German manuscripts of the later Middle Ages, and also in many printed texts of the early modern period, the superscript <e> still had a form which would be recognisable to us as an <e>. However, in the forms of handwriting which emerged in the early modern period (of which Sütterlin is the latest and best known example), the letter <e> had two strong vertical lines, and the superscript <e> looked like two tiny strokes. Gradually these strokes were reduced to dots, and as early as the 16th century we find this handwritten convention being transferred sporadically to printed texts too.

To me it makes absolutely sense that a "superscript-e" was used to express a change in pronunciation. Especially because a similair "sound" is written as æ in Danish. Could there be any relation between those two glyphs?

Yes, that makes sense. ä and æ have something in common, both show some kind of combination of a and e. But this does not necessarily have anything to do with them denoting similar sounds (although they are indeed similar in German 'ä' and Danish 'æ'.
Also, there are different ways of describing sounds (most commonly, the IPA is used, see Wikipedia: IPA vowel chart.
Moreover, on the German keyboard layout on the Mac, ä and æ are positioned on the same key, only æ can be accessed with the alt modifier key, so they must have something in common ;-)

Just for the record, the primary/initial/original form of the umlaut was the superscript e. In the inital years of German print, both in fraktur and antiqua you'll find it solely. In print however it was replaced by double dots pretty soon. The latest you could find O WITH SUPERSCRIPT E for umlaut in Antiqua would be (cca.) early to mid 18th century.

The argument of Sütterlin is really highly anachronistic, though similar mechanisms might have influenced the coice of diacritic when replacing superscript e.

You can't make an umlaut without breaking eggs!

This excerpt:

The typographers who created the Schwabacher font in 1481 picked up this style and included a small “e” above their vowels in the type case. This simplified into a little open “o” in some font designs. The double dot likely originated from a long script “e” that looked like two loops in handwriting and eventually became the standard symbol for the umlaut.

from:

http://clicknation.com/snoof/stuff/umlaut.pdf

Another excerpt from the link above:

English is promiscuous in its pronunciations: the classic “tough, cough, bough, though, through” with its variations of silent letters and dipthongs. Germanic languages are much more regular. The umlaut properly speaking is a sound, as well as the symbol for the sound. The umlaut (literally “around sound”) is a vowel that is pronounced differently because once upon a time it was followed by another vowel. The old vowel no longer appears in the word, but it still affects the remaining vowel. This process is also called vowel mutation. So the sound caused by ai, oi and ui mutated into umlaut ä, ö, and ü, alternatively written as ae, oe, and ue. A German example is the word mann (man in English), pronounced like “mahn,” becoming the plural männer (men), pronounced much closer to “mainer.” English has some Teutonic roots through Anglo-Saxon and the umlaut mutation explains how the plural of mouse is mice, tooth is teeth and goose is geese.