The Central Park Rangers are the tertiary antagonists of Elf (aside from Fulton Greenway). They mount themselves on horses for transportation.
Role in the film
They appear in the climax to chase Santa for "putting them on the naughty list and they never forgive him" and Buddy for trespassing in the Central Park. Unfortunately for them, they didn't catch him. For some reasons:
The horses got tripped by the invisible line (unnoticed by the Rangers)
They nearly caught Santa and Buddy while they're running, but they managed to escape thanks to Jovie and the people (including Walter Hobbs) restoring the Christmas spirit by singing "Santa Claus is Coming to Town".
In the animated remake Elf Buddy's Musical Christmas, the rangers were replaced by the naughty list kids.