Is it possible to install and run Exchange Management console (for Exchange 2010) on my laptop and connect to a remote exchange server?
This would save me having to RDP into the remote exchange box (I'd just need to be on the VPN).
Yes. This is possible. Install the Exchange Management Tools.
Edit: Vista, 7, or 2008 only. Here's a technet link: http://technet.microsoft.com/en-us/library/bb232090.aspx