A lot of the soviet "Artic" MR regiments were MT-LB based - it is apparently much better in slush etc as it has a lower ground pressure (not modelled in SP).
Also these days there are very few "Leg only" infantry (actually, plenty of trucks in the support echelon). But the Soviets went over pretty much 100% to motor rifle or mech rifle infantry post WW2, in a
big way - primarily because of nuclear and chemical warfare. Armoured transports at least get you through the slime and rads a bit more quickly, and if they have CRBN protection (which came with the roofed later model APC, but not the original open-topped tin truck 1/2 platoon types of the 50s), decent protection at least until you crack the hatches.
There is a fair amount of leg component in the para regiments, and trucks once air-mobiled in or simply driven behind the ground push to link up later.
The Spetznatz (more like UK commandos than SAS equivalents really) are about the only "leg" battalions. And even they will sometimes scrounge APCs if needed. They do have higher priority for any helo lift that is going spare, I'd imagine.
For a helo desant mission they take a normal motor rifle Bn or regt away from their transports for the operation and plan to marry them up with them again later (the drivers will be left behind, along with the trucks and their crews in the support echelon and the tanks and other AFVs from the MRR as well).
BUT - some of the really low schedule formations (C and D?) were planned to take up civilian trucks as their mounts, if there were any left over from other needs. These were the formations that would have the old stored T-34s etc. So Cat C and lower may well end up as Ww2 type "leg" grunts, but you would only see those in a full-on long war as they would need IIRC 6+ months to constitute and so would probably be more of an internal security item, since the planet would be glowing in the dark by then!
. But these deep reserves you aren't going to see in your situation.