I was surprised when I read your link over Germany because none of that word "Pelzmärtel" on the list but Christkind, Weihnachtsmann & Nikolaus, RedFox...
I searched to find out about Pelzmärtel in English website but I can't find them... I'm surprised to know that Pelzmärtel is not important to the world.
I find no English for Pelzmärtel to translate... It's similar as Claus Santa.
Well we have 2 different Claus Santa accord religions ground here in Germany. Evangelistic/Protestants Germans celebrate with Lantern - songs and meet and greet Pelzmärtel on the street at 11th November every year like this.
http://www.hannesrall.com/illustration/bilder_kinder_2_6/grossbilder/Laterne-4c-4.jpg
They received packet of oranges, nuts, chocolates, lebkuchen (gingerbread) etc. from Pelzmärtel (Claus Santa). We have hot Gluehwein & children punch to serve with hot wienerwurst with roll, mustard to celebrate on the street - (Of course other beliefs are welcome to join them). This is Martinstag (St. Martin's Day)
Those hot drink to keep our body warm during cold weather. Children punch for children and Gluehweine for adult are everywhere between November and January - they sells at every Christmas markets. mmmmhhhh
Receipe
Kinder punsch (Children punch)
http://www.germany-info.org/relaunch/culture/life/kinder-punsch.html
receipe Gluehwein
http://drink.allrecipes.com/AZ/Glhwin.asp
I involved with them every year since kindergarten to school.
Catholic Germans celebrate at Nikolaus Day on 6th December every year. We don't involve with them but Pelzmärtel and Lantern at 11th November.
I would say yes, Santa Claus come from kind of religious.