Have to agree with Lowtimer that open cockpit flying should not be restricted to the summer. I had my first flight in a microlight in the first week of March and, while it was a bit cold, it was nothing that appropriate clothing couldn't sort out.
Back on topic, does a Tiger really count as something a bit different? Yes, they're not your usual training a/c, but if you really want something your mates down the flying club don't have in their logbook, try a harvard or stearman, or even a gyrothingummy. Can't fault the suggestion of a Chipmunk flight though.
Ooh, just had a thought: how about the AN2 at Wellesbourne? I'm sure you could find some willing volunteers to make up numbers.