He was originally intended to. He appears in the audience of the courtroom scene briefly then disappears. During filming, the scene was changed to draw more of a parallel to the first movie ballroom scene with the three original Ghostbusters who started the business. Fan speculations have ranged from... Winston having another commitment or job to attend. Not wanting to get in trouble with the law by violating the restraining order preventing them from busting ghosts. There were only three proton packs. He helps calm people and keep order outside the courtroom. The ghostly energy sealed the room and he couldn't get in. While the above are good answers, the movie itself explains Winston's absence indirectly but with several clues. At this point in the movie, the ghostbusters no longer exist as a group or company. That is established in the birthday scene, with Winston himself stating that they are finished. The discovery of the river of slime was an accident based on doing a favor for Dana, which involved Egon with help from Ray, until Peter forced his way in. They were the three who caused the damage and were ordered to appear in court. Still not officially ghostbusters, Winston would most likely have another job commitment or whatever, but would make an appearance in court to show support to his friends and coworkers. Still, at this point, nobody would know that ghosts would appear and as stated, everything on the table was taken from their truck. They weren't actively ghostbusters, just investigating as Louis tried to incoherently explain. With only 3 proton packs in the room at the time the Scoleri brothers were released, Winston would be unable to help and is seen helping direct traffic out of the courtroom as well as shutting the doors at one point while the other guys are trying to get the packs on. It happens very quickly in the background. So, until the restraining order is lifted, and the original three are able to be back in business, Winston (our everyman) is just a regular in the courtroom still.
