hi! The mente is the name of the jacket coat on his shoulder. Its maybe should be a bit bigger size too. It was used to cover the hand with the lead/reins against cuts, but it was a cold/wet weather coat as well.
By the hungarian and crobotian grenzers it was common to use blacked sheepskin as trimmings and cover on the csákó, - i think the varazdiner csákó had to be the same style. Russo hussars and serbian pandours did the same too, but with fox and boar fur by the nco's cap. The picture you posted as your main reference image is very good. A worn and long time used covered csákó should look like that.
The hairs and all the locks defended the neck from cuts. To do so, the locks had to be enough long to lead down the blades a bit. They never chalked or washed that locks!
Who swear by the riding and hitting around with sabers, bite its tongue and smash his teeths together xD
Well actually they did bite hard on a piece of leather belt or on they csákos chinstrap! Hungarians, prussians, english, russians, even the spanish did the same. Maybe varazdiners not always, but..