1. A method in a computing system for providing pooled terminal emulation sessions for access to menu-driven legacy application tasks on a host computing system, comprising: receiving a first request from a client computing system to run an identified legacy application task; causing a first host session to be allocated on the host computing system; assigning a task identifier to the allocated first host session and associating the task identifier with the legacy application task identified in the first request; causing the legacy application task identified in the first request to be executed in the allocated first host session on the host computing device; and forwarding to the client computing system the task identifier assigned to the legacy application task identified in the first request.