Our star system has only a single asteroid belt, so if you are referring to it then the proper phrasing would be "the asteroid belt" (like "the moon" and "the sun"). And no, we (assuming that "we" is the Earth) do not pass through it at all.

If you are suggesting that we are passing through another asteroid belt, like the ones around Vega or Fomalhaut, then the damage done by passing so close to their star would far outpace the damage done by their asteroid belt!