As good as the idea sounds, it will be expensive, cause major disruption and take at least several years to complete. With all the additional work going on on the airfield (T5C which is nearing completion and LHR East) the project, if any, would have to wait. It would probably be much easier (and cheaper!) to build a new airport and have a system like this installed.

Its also a question of whether or not it is necessary. LHR doesn't get a lot of what happened last year with the snow compared to other airports such as those in Norway etc. As Sixth Freedom said, snow ploughs should be enough at LHR, they just need more!