Executing command remotely with ssh, and PATH

[Colin Law]

There is apparently something I am not understanding about ssh or
environment variables.  I can execute a command remotely using ssh,
something like
ssh remote_server "command_to_execute"
and that works ok.  However in another case I need to add to the path
before executing the command so I to test the concept I tried
ssh remote_server "PATH=/some/path:$PATH; echo $PATH"
but it just shows the original path.  If I login to the remote server
and copy/paste the above command then it shows the extended path as
expected.

Can anyone put me straight?

Colin