So I'm looking in the .gsc file and I see these lines:

game["allies_soldiertype"] = "woodland";
game["axis_soldiertype"] = "woodland";

And I started wondering... is there a way to change that "woodland" to something else so it would give every class the ghillie suit, and not just those with a primary weapon as a sniper rifle?

You'd have to change the all character files (raw\character) for each of the mptypes you want to have the ghillie suit to this:

// THIS FILE IS AUTOGENERATED, DO NOT MODIFY
main()
{
	self setModel("body_mp_usmc_woodland_sniper");
	self attach("head_mp_usmc_ghillie", "", true);
	self setViewmodel("viewhands_marine_sniper");
	self.voice = "british";
}

precache()
{
	precacheModel("body_mp_usmc_woodland_sniper");
	precacheModel("head_mp_usmc_ghillie");
	precacheModel("viewhands_marine_sniper");
}

except that you'd set "self.voice =" to whatever nationality is appropriate. Even though some of the variables above have "usmc" in them, they're used to make the ghillie suit on the Spetznaz vs. SAS maps.

N.B. I'm all but certain that you'll have to pack the modded .gsc's into a fast file. It probably won't work with an .iwd, since the stock character files are in packed in the game's .ff's. That in turn probably means you're going to have to add several lines to your mod.csv for each modded character type

character,character_mp_sas_urban_recon 

- and so on, and add one line in makeMod.bat to grab the new character files

xcopy character ..\..\raw\character /SY

It would be a pain in the buttocks, but doable.