Can we do multivariate time series analysis using holt-winter ( Exponential smoothing) method? Just like we have a method like ARIMAX and SARIMAX where we can provide exog and endog variable for perfroming multivariate analysis. I was hoping is there a way, we can achieve same using ETS as well. Please let me know in case any has worked on this.
Exponential smoothing is usually defined on univariate data with no exogenous variables (see e.g. this book).

However, Rob Hyndman discusses different approaches of including exogenous variables in this blog post and gives some more references.