No, not everybody had a tractor - that would be ineffective, given how many small family-owned farms there were. But they did use tractors and combine harvesters. TBH I don't know whether they were shared between neighbors or just unofficially borrowed(#) for a bottle of vodka from the state farms (PGR).
(#)There's this Polish verb "załatwić" which I cannot properly translate to English. It means obtaining products or services using ones connections, cunning and possibly transfer of a usual token of appreciation as in "załatwić za flachę" (obtain something in exchange for a bottle of vodka).
EDIT: Then again, maybe not. When I hear people in Poland use that word, I'd maybe translate it as "organise" or "arrange", but only in the sense of arranging the acquirement of something.
Overall the gap was more along the lines of big cities vs. province as you say; rather than geographical. In a centrally planned economy large urban centers were overprivileged in the pecking order.
(not that there is anything wrong with it)