HOTEL counters were off to a quiet start in the first trading day of 1993 yesterday, but this did not dampen analysts' optimism for bright business prospects within the next two years. Yesterday's stock market trading was the slowest since December 31, 1991. But Sun Hung Kai Research analyst Brian Oung said the slow trading was to be expected for the first week of the new year. It did not change his optimistic forecast for Hongkong's hotel industry. ''1993 will be a good year for the hotel industry and 1994 will even be better in terms of profit, occupancy rates and ability to raise room rates,'' said Mr Oung.