Mule paths have always been an interesting but minor issue in tagging. In the English Pennines there are many pack horse trails, often with distinctive bridges. There is a mule trail, the [Bright Angel Trail][1] down to the bottom of the Grand Canyon, which is very narrow. There are many in Alpine areas too. I can also think of old mule paths in [Glarus][2], and up the hillside from [Belgirate][3]. I've never been able to map these because they are totally shaded by trees.
I think there are three basic/fundamental types of highways, that have existed in one form or another since mankind domesticated the horse: for 4-wheeled vehicles (roads/tracks), people on horseback (bridleways) and people on foot. (Obviously there are more recent special cases such as motorways and cycleways; I might be wrong but I don't believe [wheelbarrows][4] ever received dedicated highways).
Mule paths must belong to one or other of the latter categories. If they are not passable by a person on horseback I would suggest that they must be footway/path (according to choice). Obviously many old mule paths are wide enough now for 4-wheel vehicles and may be graded as tracks.
Therefore in your case I would
- **tag this as a footway/path.** If it's not suitable for horses it's not a bridleway. (Bridleways not signposted as such can be recognised by higher clearance of any foliage, wider curves etc.)
- **add a historic tag** something like historic=mule_path, with possibly an adjectival tag to show that it belongs to the kalderimi (not sure if this s is good greek) class of these things.
Lastly these the class of pack animal trails is of particular significance in the context of Historical mapping, and specifically in the pre-Columbus Americas where there were no wheeled vehicles.
[1]: http://en.wikipedia.org/wiki/Bright_Angel_Trail
[2]: http://www.openstreetmap.org/#map=16/46.9615/9.0943
[3]: http://www.openstreetmap.org/#map=16/45.8446/8.5664
[4]: http://en.wikipedia.org/wiki/Wheelbarrow#Ancient_China
