Mexico:
Division De Cuba is not just the division but all the other Technical Specialists and several Sailors and Airmen whose vessels were grounded there, due to enemy action making it impossible for them to escape and survive. Vessels damaged that could make port but could not go much further, they couldn't cross the Atlantic let alone cross it and deal with a fight should they encounter Nato assets. However, they could make for the mainland! <Think of a Russian Version of Going Home> And thus you have a force of a Division of regular combat troops plus a second Division of technical specialists, civilians and naval and air personel as well.
We toss in other Russian Refugees who were given the word to go to Cuba or Mexico when hostilities began, so they now have a group of say 100k consisting of about 30 or 40K military, another 20k of civilian specialists and government workers and the rest would be their families or families, freinds, supporters and servants.
I would also toss in the whole civil war in mexico as a good thing plotwise.
As for getting involved without Nukes,
Add a Division sized group of specialists and military and their family to help the mexi's develope and protect their oil assets so they can supply the russians with oil, maybe even a naval and air instilation as well so that adds another 10 or 20k people.
The US not wanting to stand for that sends in some light forces to sieze or damage some of their oil assets. After all times are desperate, and that oil would do ALOT to aleivate the problems at home. However, the mexi's are not thrilled with the idea even if they are to be paid, so they respond, Ivan joins in <although their housing russians forces in the region could make them an ally and combatant>
And also, mexican forces begin raiding the US Southwest taking advantage of the chaos, locals defend themselves so the mexi's get bigger and bolder, the US sends forces and before long the two sides are clashing, some of the bandits are actual mexican army forces, and here we are! Then, there could be a series of expeditions on either side going deep across the boarder conducting raids. This culminates in some full scale battles on both sides of the border, however the mexis manage to muster forces spearheaded by russian forces and they make their move into the US SW. This is also coordinated with the russian forces in Alaska, a few long range patrols comming S. to open lines of communication and link up. The actual link is minimal, but the whole idea of being able to contact freindly forces is a huge moral builder. From there, my concept is they manage to link up somewhere and either establish a self sustaining defendable catonment, and/or plan a way to get back home. \
Here is an idea, the Sovs head for the mothball fleet at Sussion Bay S. of Frisco and want to bring a couple of the larger vessels online to sail home in. A little far fetched but it would make for a good campaign, russian colony in the middle of the West or Pacific Northwest would be wild.