Your existing PvE gear should be completely useable in PvP. some stats may be irrelevant, and therefore those items will not be optimal for PvP, but you should be able to wear what you want when you want. Arbitrary restrictions based on where you are are not a good idea.

If you couldn't do this, you'd have to start out naked or buy a special set of gear before you even play pvp for the first time, so that's one reason why it's not a good idea.