Context properties (those which displayed from HAT as MessageDetails->Context->...) include both promoted and accordingly accessible within orchestration and not promoted.  As Jon Flander notes, only promoted properties are used for subscription services and hence originally promoted. The following table maps the promoted properties to the compiled schema classes.

Property Name	Orchestration Access	Namespace
InboundTransportType	BTS.InboundTransportType	http://schemas.microsoft.com/BizTalk/2003/system-properties
InboundTransportLocation	BTS.InboundTransportLocation	http://schemas.microsoft.com/BizTalk/2003/system-properties
MessageType	BTS.MessageType	http://schemas.microsoft.com/BizTalk/2003/system-properties
ReceivePortID	BTS.ReceivePortID	http://schemas.microsoft.com/BizTalk/2003/system-properties
ReceivePortName	BTS.ReceivePortName	http://schemas.microsoft.com/BizTalk/2003/system-properties

The question is how to access the rest of the context properties which were not promoted? Well, these properties mostly  used internally by BizTalk Messaging Engine, however, from the pipeline they are accessible pretty easy. Stephen Kaufman wrote a exciting post about this issue.