well there is a series out there that has done this feud (kinda like how dark knight is its own series..ect) and i know the end result, hoping its got some twists in the adaptation here, tho the original series was pretty good on its own, but could potentially kill 1 franchise with a clear cut winner. Due to the movies subtitle have a feeling its the start to a justice league counter to marvel's Avengers success, which has me again hopeful, the B vs S is only a part to the story and the back end is B with S and seeing the need to work together and expand.
As for the freeze, Batman is fully aware of all of Superman's abilities, he showcases them a ton and is constantly in the media eye with Lois and the Daily Planet on his heroic deeds. The suit most likely has a temperature control system that keeps bruce wayne from freezing or burning up if he used his eye lasers. If the exterior became an ice cube. the suit could probably heat up or break out with sheer strength from its enhancements. Mr. Freeze could never keep batman down even in his tights lol
Due to its dark portrayal in the trailer, and the ppls turn on Superman, Im leaning towards Superman crossed the bay into Gotham, where he might not be as welcomed as he is in Metropolis, and that also pisses batman off.