Hello,
I am planning to buy call of duty modern warfare 2 ROW version as it is the only one available on steam, would like to know if the trainer is compatible with steam and also would will i be down loading the 64 or the 32 bit version from steam and which version does the trainer support?
Hello. 
The ROW (“Rest Of the World”) version of Modern Warfare 2 is designed for those countries which have censored the original game (cough-Russia-cough) because they didn’t like being portrayed as the baddies in the game.
If you can legally purchase the original game in your country, there is no need for you to get the ROW version. The only differences between them are that the ROW version is edited to bypass the Russian (etc) censorship system. And I believe one of the campaign missions was removed entirely from the ROW version.
Whether the game is 32-bit or 64-bit generally depends on how much RAM it requires.
Games that require less than 4GB RAM are generally 32-bit. Games that require 4GB RAM or more are always 64-bit.
The trainer may or may not work. But I’m leaning more on the “won’t work” side, since the ROW version is heavily edited and therefore may not be compatible with the trainer that was made for the original version.