I've not read too much into the Clan societies but I always had my own (read: MY OWN) interpretation which is possibly far from what the Clans actually are. It's always been about the culture for me as opposed to how the Clans hierarchy is laid out and such. I have a vivid imagination so I like to envision all that I read and create how a character looks exactly for me the first time I read of them, it helps things to play out as a film reel in my head rather than just a block of fictional text. This is my interpretative vision, not from the established canon.
From the days of playing MW2 I've always envisioned the Clans to be very tribal in nature, very reminiscent of their namesakes. Clan Wolf warriors have always been rooted thoroughly in my mind as brooding burly warriors with flame red or braided blonde hair, piercing blue eyes and favouring knotted tattoos and copious amounts of alcohol. I had the idea that both Wolf and Ghost Bear, the latter being very much more Norse in nature, are modelled after our own Celtic societies from history. I see them regaling younger warriors with great sagas about their Khans and Star Captains around a cloistered fire, built in the centre of their ring of powered down 'Mechs on some world they were conquering, all sharing a cask of ale. I see their culture based in the prowess of their warriors, much in the way of the old world but the warriors wouldn't be warriors without the lower castes. It is the common people who pave the way to war after all and I see the Wolves venerating this, so that the Warriors are more mingled with their common brethren as opposed to being aloof.
I see Clan Jade Falcon to be very oriental in nature, almost entirely opposite of the rustic, raw power of the Wolves or the Ghost Bears. I see them as very defined people, slim and physically fit, built for stamina, not brawn unlike the Wolves. I see a healthy mix of the Samurai ethos mixing through their society, how the Warriors are the be all and end all, their word is law for they are the dominant caste of the society. The others are well provided for by their warriors and in this the warriors are afforded their arrogance and high station. I see them as very serious people, preferable to symmetry and the philosophies of war rather than the loud and brawl prone Wolves. I see great temples on their worlds, with fluted roofs and statues of sweeping Falcons made from jade stone. I see their culture as a very isolated and believing utterly that their way is law, above all.
I see Clan Smoke Jaguar as being people of dusky skin, dark hairs and serious temperament. Based a lot on the old Aztec and Mayan civilisations of our history. I see them as being honour bound to the point that it dictates every action in their lives, even more so than Jade Falcon. That a Warriors words never come lightly for they will be carried out to the literal letter. I see the Warriors as quiet, hard people, their achievements festooned upon their body and their 'Mechs in the forms of jewellery and tribal markings, almost like the Inca Hieroglyphs. Telling an entire story just with one image. I see the warriors not as aloof like the Jade Falcon, or the humanitarians of the Wolves. I see the Smoke Jaguar warriors to be almost godlike, completely separate from their nation but in no way out of harmony with their civilisation. I see them almost like the Sumo of Japan, they are regarded with such super human idol-ism and admiration simply for their way of life but they aren't held above the common man in any superior form. They are to be respected, possibly even admired but never feared for they are just as much a part of your world as you are of theirs. I see the Smoke Jaguar warriors bringing new worlds for the people, for the Clan, not for their Khan or the view of the Star League.
I have skewered images of the other Clans as well, which will shape the more I read into the various source books and combat doctrines and what not.
It's why I see Clan Jade Wolf as the bastard culture crash of Falcon and Wolf. I see the warriors striving to greater feats to out shine their fellow warriors from the old Clans. I see them as young, rash, enthusiastic fighters holding aloft the banners of their failed fathers. Fighting the cause so many have forgotten. Almost like a head strong group of young knights pushing past the seasoned veterans for their bitter taste of the glory.
I've been very tempted to start writing my own fan fiction on the journey of Clan Jade Wolf and its exploits, based on the league drop 'Battle for the Inner Sphere' and the more recent friendly drop with the Vegan Rangers. This is the kind of examples I'll be using to describe the warriors of Clan Jade Wolf and their interactions with the other Clans and the Inner Sphere houses and units.
As I said though, this is my view on the culture of the Clans, not exactly their doctrine or how they actually work.