How can I set up a private forum for people to upload videos

Folks can make private videos on YouTube but you'll need to have them shared with you, as I recall. But that should keep them from being displayed otherwise. Then they can plonk the links into a separate event page.

But maybe I'm not understanding you. Do you want the videos to be only shown to the group or only shown to you (and then you pick a winner, which you presumably release to the group later)?

Thanks for you reply

Yes we just want admin to be able to see he videos until we pick s winner. Ideally on facebook as that's were our users are

There doesn't seem to be any sort of a good way of doing this. But I'm sure there are sites which can do this. HubSpot (they're very reputable; follow them if you want to learn about social media) has a list here -
http://blog.hubspot.com/blog/tabid/6307/bid/33352/Everything-You-Need-to-Run-a-Successful-Social-Media-Contest.aspx

Note that that blog post is from 2012 so some of the third-party providers they are listing probably don't exist anymore. The advice to check and make sure you're following Facebook's rules - yeah, that would be a good thing to do, too.

Consider the scalability of this venture, too. Can you do it if 50 people enter? Maybe that's not a problem for you, but do consider the effort involved if the contest blows up and becomes extremely popular.