Very good question. Exchange Active Sync (EAS) does not allow that on the server side, but perhaps you could set some policies (rules) in Outlook? I think the email gets pulled off the server though and gets to the phone before it hits your inbox.
Ok, I just looked at Touchdown for EAS, which is what I use. You can create a rule in Advanced settings that will mimic what you can do in Outlook, i.e. move a particular email to a folder, etc. Perhaps that might be what you are looking for.

 

In Outlook it's under, Tools > rules. But I still think it will hit your phone before it hits Outlook. EAS doesn't care if you use OWA or the client version. You should check in the Activesync email app on the phone. Since I don't use that I really have no way of knowing. Touchdown is great but expensive. I needed it due to multiple AS email accounts which the native email app will not support. I think it's a Microsoft licensing thing.