Every outdoor party needs a huge bonfire! It's part of the ritual. Depending on your definition of "big", you might be able to get around the hot-logs-on-ice problem using propane gas burners - I've been using them for years to get around summertime burn bans and the risk of grass fires. It might not be as romantic as the traditional bonfire, but it's a lot better than nothing and it really helps keep people out on the dance floor all night. I started out with one of these, and the system I'm using now is just a scaled-up version of the same idea:

https://www.campingworld.com/portable-propane-outdoor-fire-p...

Seems like it might work for a frozen-lake party, since the heat stays up off the ground; you could throw a reflective insulating blanket underneath for even better results.