In the first Die Hard (1988), John McClane only had a few scripted one-liners. However, Bruce Willis ad-libbed many one-liners, and audiences liked them. So much so that in this sequel (and the next one), more gags were added, and Willis was told he could ad-lib as much as he saw fit.
The scenes with Bruce Willis running through tunnels under the airport were filmed at a water treatment facility near Los Angeles. The facility has miles of underground tunnels, and was also used in Live Free or Die Hard (2007), doubling as the Woodlawn Social Security Administration building.
Denver was unseasonably snowless during the shooting of the snowstorm scenes and a fair amount of snow had to be created artificially.