running iceweasel on remote host seems wrong

[Miernik <public@miernik.name>]

Strange problem. I have two debian machines, one local at home, and one
remote somewhere. At home I am connected behind a NAT, and the remote
machine has a public IP.

I want to run iceweasel on the remote machine, and let it display on my
local machine. I have iceweasels installed on both machines.

So from the local machine I do:

ssh -Cv user@remote.machine.name.tld -X

After a while I get a prompt of the remote machine, looks OK, ls gives
me listing of files on that machine.

env shows DISPLAY=localhost:10.0

So I run 'iceweasel' there. And after some time I get it displayed,
but... it seems that it runs it somehow on my local machine, for example
file:///
displays the root directory of my local machine, not the remote one, and
when I browse, with tcpdump I see HTTP traffic, and not SSH traffic as I
expected.

I don't understand it. How I am supposed to run iceweasel on the remote
machine (using only the local display), so it would work as it would be
sitting at the remote machine?

-- 
Miernik
http://miernik.name/