My daughter went into town last week and used her Zip Oyster
throughout. She traveled from Cheam to Green Park (via Victoria), and
returned to Worcester Park (then bus back to Cheam) due to the snow.
Note: Southern trains ran a limited timetable on the Friday, and
announced in the morning that trains would stop running shortly after
7pm. Separate gripe. The weather didn't get worse that day - in fact
it got better - a service could have been maintained until much later
- but I digress.

My daughter ended up being charged the full £7.50 adult day travelcard
rate (Z1-5). On doing some research, I discovered that Southern (and
SWT) do not participate in Oyster discounts for such 'students' - so
they are not fully signed up to Oyster. Secondly, if she had routed
via Vauxhall (via a change at Clapham Junction) and not Victoria, she
would have been charged about £1 less per train journey. Why?