Can I wear a helmet camera in an open cockpit?
It's certainly possible to use a GoPro in a Tiger Moth: there are plenty of videos online to prove it. That means the question is, is it legal and if so how to do it safely?

Legally, there isn't anything relevant that I could find on the UK's CAA site (your profile says you're in the UK), but in any case most discussions on cameras in GA aircraft have been about attaching a camera to the aircraft, not to the pilot (see this question, for example). For obvious reasons, it's difficult for any aviation authority to regulate what pilots wear or carry on their person and if there are no specific regulations that means that only the general don't do anything stupid or dangerous rule would apply. I assume that the UK has something equivalent to 14 CFR 91.13 in the US:


  No person may operate an aircraft in a careless or reckless manner so
  as to endanger the life or property of another.


(Note: I'm ignoring any contractual issues here, like what your insurance company or FBO allows.)

From a safety point of view, the main risk of a portable camera is that it comes loose and ends up blocking a control surface externally (e.g. wedging in the rudder or elevators) or a control internally (e.g. falling to the floor and getting stuck behind a rudder pedal).

One specific concern with a helmet-mounted camera is that if it does fall off then it's very close to your face and it could obstruct your vision or even just startle you, which would probably be bad news on short final with a gusting crosswind. (Pilot distraction from operating the camera controls is another potential issue but that's true of any gadget.)

Ultimately I would say it comes down to how confident you are that the camera is secure and not going to get in your way: if you are, then go for it. I don't think the attachment issues are significantly different from skiing, parachuting, driving sports cars etc. with a helmet camera, and that happens all the time. And cameras are a great tool for reviewing and improving your performance (especially if you have full audio too), which makes the 'risk' very worthwhile, in my opinion.