Does the camera itself reach below-freezing, or is it just outside? If you keep the camera warm (usually it won't hit freezing because it'll be in your hands, coat, bag, etc) the batteries shouldn't slow/diminish. (But yes most types of batteries used, Alkalines particularly, don't last as long or effective when in the cold).
Cold weather can affect most electronic components, especially where the voltage needs to remain stable for operation.
PS: If it's a Real dry cold, you could get static electricity discharge showing up across your film as lighting bolts. But I've only ever seen that with electronic film advances where the film zips by much faster than hand cranks.
Film (Working RF): Canon 7, Fed-2A, Argus C3, Mercury II
Digital: Olympus E-M5, E-P3