Were they collectivized like those of the USSR? And what were they like during the Cold War? Old-fashioned? Modernized?

Following the Soviet example, most Eastern European communist regimes did collectivized their agriculture after WW2 (Poland is an exception though).
As for modernization, it varied from country to country. By the '80's, some of these countries (Hungary for example) had developed and efficient agriculture sectors producing high quality products.

East Germany had the "LPG" or Landwirtschaftliche Productions Genossenschaft ( Agricultural Production Cooperative)

https://en.wikipedia.org/wiki/Landwirtschaftliche_Produktionsgenossenschaft

As with all parts of the GDR economy it worked perfectly and they achieved Ulbrichs target of "Überholen ohne Einzuholen" (Overtake without catching up) perfectly giving the GDR citizen not only excellent vehicles like Trabant and Wartburg but also prime GDR beef and tomatos