Yes, a separate vignette is required for trailers and pulled caravans weighing up to 3.5 tons.
The same applies to motorhomes with trailers. The trailer always needs its own vignette.
Any vehicles and trailers over 3.5 tonnes are subject to the LSVA / PSVA.
Related articles:
What vehicles need a Swiss motorway vignette?
Where can I buy the Swiss motorway vignette?
What happens if I drive without a Swiss vignette?
How much does the Swiss Motorway Vignette cost?
Are shorter term Swiss motorway vignettes available (daily/weekly/monthy)?