I've actually spent a great deal of time on the perimeter road around LHR (don't ask) and concur with a lot fo what's been said above.

You can't walk to T1/2/3 (AKA 'Heathrow Central'). You can, however, take a free bus from many places around it. There is a zone (I can't remember the exact details but it says it on all of the bus-stop sign posts where this applies) within which bus drivers will take you to the Heathrow Central bus terminal for free.

You can definitely walk to T4.

Like the others, I'm not sure about T5. It's so far away from everything, I've never tried to walk there before.