No, Trinidad and Tobago has never recorded snowfall. The twin-island nation lies at 10–11°N latitude, just south of the Caribbean's hurricane belt and firmly in the tropics.
Snow requires freezing temperatures at surface level. In Trinidad & Tobago, the coldest recorded temps are ~18°C (64°F) at high elevations during rare cold fronts. The freezing level in the tropical atmosphere typically sits above 4,500 m (15,000 ft)—well above any terrain.
Frost, sleet, and snow are meteorologically excluded. The islands' "winter" is simply a slightly cooler, drier season.