The crew had foggy mornings just on the days they needed them, and the fog lingered only so long as it was needed to complete the scenes. Snow was written in the script for one sequence, never really thinking that it would actually happen. It normally snows hard enough to actually be visible on film 4 or 5 times a year. When they needed it, the snow came down in huge flakes just until the director said "Cut" on the last take, and then it stopped.
The bus used to take Neale out of the park in the movie was a decommissioned local bus purchased at auction. This specific bus was in service 1991-2 and on the same route that Neale had to travel to get to work, and was thus almost certainly one of the very buses that Neale had taken during the real events depicted in the movie.