Meteors are much closer to the sun - the asteroid belt is between Mars and Jupiter only 3-4 times as far from the sun as we are - right next door in solar system terms.
The comets are in the Oort cloud about 50,000 times as far from the sun as us. At this distance the temperature is low enough that water and pretty much all 'gases' are solids.
Also there isn't much out there except comets so while all the space ice/dust/rock etc in the inner solar system has been swept up by hitting passing planets, out there it is undisturbed unless picked up by a comet.
We only see comets when one of them is disturbed somehow and begins to fall toward the sun. Most pass by the sun and head back out to the cloud on a very long period orbit. Only a very few are caught in an orbit that brings them back quickly like halley.