It seems to be impossible.
(I'm talking about changing the language in the program options, menus, etc.)
Does anyone have a work-around?
Is this option available in Firefox?
My need is specific: I use Firefox/Iceweasel only for Zotero (a citation management program), it would be useful for me to be able to switch back and forth between English and Russian to see what it's talking about.
Thanks in advance!

gets the russian language package.
Then you switch from current language->any other language package installed, by Edit->Preferences-> Main : Manage Add-ons... -> Languages : Enable/disable LANGUAGE_NAME. It asks to restart iceweasel.
I know, not very convenient...

I got so tired of iceweasel I changed to google-chrome. At least it's a lot faster. Although having only crappy extensions is not very charming.
If you have a google account, you can synchronize your bookmarks in any other chrome, which is perhaps kind of what you are looking to do with zotero?
You'd still have to restart it to switch between languages. But it uses the LANG variable, so you can make aliases to make that faster/less annoying.

Ah. My mistake was apparently to get the Russian language version of Iceweasel to begin with.

Perhaps I could get an ENGLISH language pack for the Russian version and do that? Or perhaps I'd need to uninstall Iceweasel and then reinstall the English version and then do as you recommend.

In any event - thanks!