XDM is the most common way to log in to a graphical terminal. It a bit looks like login but it is internally totally different.
In directory /etc/X11/xdm there are configuration files that are executed on different login phases. Xstartup (and Xstartup_0 specially for screen 0) contains commands to be run after the user has logged in (commands are run as user root).
The path that is set for users is in /etc/X11/xdm/xdm-config. There are lines:
DisplayManager*userPath: /usr/local/bin:/usr/bin:/bin:/usr/bin/X11:/usr/games DisplayManager*systemPath: /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/bin/X11
That will be a default path for normal and root users respectively. It is very important that /usr/bin/X11 is available for X users. If X user logs in to another machine to start and X client application, he should get /usr/bin/X11 to his path even he don't seem to come directly from X terminal.
After running Xstartup the XDM runs /etc/X11/Xsession that is run as the final user. Local configuration is meant to be done in /etc/environment that is sourced (included) from Xsession if available (Xsession is run with /bin/sh and thus /etc/environment must be a sh file). This clashes with ssh that supposes that /etc/environment is a file that contains just lines of form VAR=VALUE.
By default the path for all the commands invoked from X window manager menus is the path inherited from XDM. To use something different it must be set explicitly. To start a terminal emulator with a path that is "normal" some special option must be used. In xterm the option -ls (login shell) must be used to get a login shell with path specified in shell login initialization files.
Window manager inherits environment of XDM. All the programs started by the window manager inherit the environment of the window manager.
User shell environment does not affect the programs that are started from window manager buttons and menus. For example, if program is started from 'xterm -ls', it has the default environment of login shell but if it is started from menu, it has just environment of the window manager.