Gebirgsjäger research - Helmets and camo

As I want to try to depict my little lead dudes pretty close to history I like to do some research.
When it comes to the Gebirgsjägers, I found them a bit dull and repetetive albeit very nicely sculpted with everyone wearing a field cap.

Most wide spread pictures of Heer-GJ shows them in their Bergmütze, but did they use it in combat too?


So after several hours of Google-Fu, I came up with these conclusions:
Helmet is used in combat, exceptions are done in colder climates and mountain terrain.
While marching, cap or bare head seem to be the preferred outfit.
Camo wind jackets, most probably not used by Heer-GJ.
Zelthbans are used in camouflage patterns.

A couple of links:
Greece
http://deutschlandsgloria.tumblr.com/post/56752140085/gebirgsjager-soldiers-fighting-around-fort-roupel

Norway
http://histomil.com/viewtopic.php?f=95&t=3918&start=3150
http://25.media.tumblr.com/a1a1b2cc77009e91dd64fcbe74adc160/tumblr_mi6y02F1pm1qbsnsoo1_1280.jpg
http://25.media.tumblr.com/266c477937035c9794e728186cc0fe0c/tumblr_mhxoovbaMa1qbsnsoo1_1280.jpg
http://ww2images.blogspot.se/2013/10/execution-of-brave-russian-prisoners.html
Zelthban example, helmets in Ukraine:
https://www.flickr.com/photos/41818881@N06/sets/72157632894241921/

Crete
https://www.tumblr.com/search/crete%20invasion#
https://41.media.tumblr.com/b3165493a0aa4f222cc2f04073acb768/tumblr_n7j8sjBsv91rcoy9ro1_1280.jpg
https://40.media.tumblr.com/82895b6c12e43eefe7a0b31ad52be57d/tumblr_n7hivztEiv1rcoy9ro1_1280.jpg

Italy
http://histomil.com/viewtopic.php?p=82901#p82901
http://upload.wikimedia.org/wikipedia/commons/8/81/Bundesarchiv_Bild_101I-316-1172-06%2C_Italien%2C_Gebirgsj%C3%A4ger_mit_schwerem_MG_42.jpg

Says it's eastern front, but I dont know if it is GJ or not:
http://media-cache-ec0.pinimg.com/736x/46/3e/99/463e994b1ee89c5e1f6d41cdb34aa8d6.jpg

Poland
http://histomil.com/viewtopic.php?p=76711#p76711

Other
http://fykse.dnsalias.com/bilder/tornfub1/fykser14.jpg
http://pinsta.me/p/960923899782375424_1573693465
http://pinsta.me/p/955282972713545898_386996147
https://reibert.info/attachments/kanone-jpg.194223/
GJ with helmet covers in camo (could be Zelthban too)
http://36.media.tumblr.com/6e83d3d46aaa8e28b574979e25cb2a1a/tumblr_mwhv5yargm1spwf52o1_1280.jpg