[Justin Stiltner]

Im going to sound old here...
back in my day before the internet when we needed to call somebody we could look them up in the phone book...

Seriously most likely your mentors are in the phone book, or will respond to e-mail. The contact info for most team mentors is on first's website. Contact your local hotel, public library, community center, YMCA, churches etc. I guarantee you can find a meeting room they will let you use. Take cardboard and stick to prototype with as well as some measuring tools.

Divide up into small teams to work on sub projects, if the weather is bad, have the geographically close people meet at each others homes to work on things.

The weather is only a roadblock if you let it be one.