Here's a thought, based on the idea of a literally cold Cold War, but semi-serious: arctic combat vehicles. Flying over the Arctic is much the same as flying over the tropics (until you get shot down and find you've got the wrong survival pack), but fighting on the ground is a WHOLE different ball game. Here's a couple of scenarios:
1. The US finds out that the Soviets are planning to send commando teams into Alaska and/or Northern Canada to attack early-warning installations immediately prior to a nuclear attack. The Soviet approach to equipping these guys is probably to give them white overalls, extra rations, and a stern lecture about how unpatriotic and counter-revolutionary it is to whinge about the cold, however the Americans being the Americans, they decide that fighting these guys on the ground obviously needs LOTS and lots of fancy new hardware.
2. The Antarctic Treaty either breaks down or never happened, so Antarctica becomes a credible war zone. Perhaps the Soviets set up a naval base on the continent from which to send subs and spy-trawlers out to monitor French and British nuclear tests or interdict shipping around the Cape, or perhaps several nations decide to put their 'last redoubt' emergency command bunkers (i.e. somewhere for Air Force One to actually
go) there and only discover the other guys after they've spent billions on the bases. Cue a race for land and borders that rapidly come to reflect the global Cold War in microcosm.
In either case, you could imagine countries building troop-carriers and 'tanks' that are a cross between snow-cats and conventional AFVs. They'd need very low ground pressure, so over-size tracks and limited armour, and they'd possibly try to eliminate the need to open hatches as much as possible, so they'd have truck-style driving positions and windowed commander's stations above the actual hatch, similar in appearance to the various Israeli 'lighthouse' modifications. You'd also need to be able to live inside them for extended periods, so they'd be larger than conventional AFVs, again with implications for armour weight.
For 'jeep' type tasks (liason, recce, light attack) aerosans would be an option, as would motorcycle-style snow-mobiles.
Some of the sci-fi multiple track-unit vehicles might form appropriate inspiration: the iconic Tucker Sno-cat does, after all, follow that form itself.
Real-world example are few and far between. The Russian MTLB has a remarkably low ground pressure, partly to address these concerns, and that's why it's also favoured by Sweden. Apart from that, there's the inevitable Volvo Bv.206 et al 'Bandwagons', the Russian WWII aerosans and er, not much else really. NATO had extensive plans to fight in Norway, and Sweden and Finland had their self-defence needs of course, but all those theatres are 'conventional terrain with a lot of snow on it', rather than 'pure snow and nothing else'.
