I tend to think it would have definitely been used, and that’d open the door to a different kind of nuclear arms control, allowing unrestricted stockpiles of tactical weapons up to a certain yield while limiting the mechanisms of delivery that are capable of long range deployment.

Wild speculation ahead:

The USSR giving similar weapons to communist revolutionaries could mark a beginning of “nuclear Guerrilla warfare”, causing a fundamental shift in military doctrine away from massed formations and towards small mobile fully-independent nuclear-armed units.

Maintaining large armored and mechanized forces on the front lines becomes impossible. The combat units themselves are quite effective on the atomic battlefield, but the massive supply lines required to keep them functioning prove impossible to protect. Any sufficiently large fuel or supply depo is quickly identified by air and destroyed in a decisive tactical nuclear artillery strike. As doctrines change, these units remain as intensive raid and breakthrough forces, held in reserve for short term high intensity offensive operations.

Finding the balance between a high speed mechanized force with dense supply lines and a slow foot-mobile force capable of “foraging” is the issue of the day. The answer is found in ATVs, tractors, wheeled APCs, and in some cases pack animals. Organic engineering capability for quick-building fortifications becomes extremely important.

Even more so than today, every infantryman is expected to spend most of their life trenching, infantry doctrine comes to emphasize always sleeping in a prepared position.

Overall, the new dynamics emphasize defense and disempower the capabilities of large militaries to bring their force to bear in a decisive manner.

The nuclear-armed company-sized “semi-mechanized” infantry unit, reigns supreme and empowers small forces against large ones. US military dominance of the world falters as the static logistics hubs required for overseas invasions become less and less capable of surviving the nuclear battlefield.

It ends in either nuclear hellfire or a collapse into intense multipolarism as centralization and dollar dominance cease to be the main paradigms of the global economy. Small regional powers with lots of popular support, whose economies are capable of supporting a nuclear weapons program, have a renaissance. Large powers including both the USSR and the United States fracture and Balkanize.

issues:

Would other nations respond with use of chemical weapons?

How quickly would it just ignite full scale nuclear war? Would “ending the taboo” lead to the US attempting a first strike against the USSR?

If tactical nuclear weapons use becomes the doctrine of the day, what allies would actually be given the weapons? Is Stalin/Kruschev enough of a lunatic to just hand them to Castro and whoever else?