Doug wrote:
> But that is you are using openSSH.
> I understand that Putty already has HTTP proxy connect build in.
> I hope my understading is correct.

Doug, your understanding is absolutely correct :-)

I just didn't know that putty has this functionality built-in. I just
tested configuring proxy in putty on a windows-machine now, and it
worked fine.

Doug wrote :

But when
> I set it up in PUTTY (under Connection -> Proxy tab) looks like the
> HTTP proxy detects I am trying to connect to SSH server. Thus it throws
> service not allowed exception (error 403).

Right, this is what I meant when saying "In a lot of setup (including
my own) the connect-method is only allowed to port 443,".

The proxy-server of your company does not allow the connect-method to
port 22.

> But if I try to change the port # of ssh server setting for PUTTY from
> 22 to 80 it throws this exception:
> 503: service unavailable.

Yes, because there's no ssh-server (not even anything at all)
responding on port 80 on the machine you try to connect to.

I think the solution to your problem was already given by Todd H. in
his previous message.

You should configure your ssh-server to listen on port 443 (maybe 80
would do too here, but 443 is better).
Of course you need to tell putty to connect to port 443 then. I just
tested this here, and it worked fine.

Cheers,
Armin

PS: Be careful with firewall-piercing if your work-contract does not
allow such habits.
Of course this ssh-connection shows up in the proxy-log.