Colleagues of mine were tasked with building a forecasting model. They intended on doing a train/test split for cross validation. I know that when training models for forecasting, a "walk forward" validation is more often used. Why is that?
While I think the comment to your post covers the 'why', what you mention is generally called a 'rolling forecast origin', which is alright for one-step forecasts.
Instead, try using a similar concept (if you have enough data) where you define a test set of length h, remove h of your most recent data points, run your models on the remaining data, record accuracy of the forecasts versus the withheld data. Then iterate the process until you run out of enough training data to build models (perhaps 3 seasonal cycles). Average the out-of-sample error results and you'll have a good idea of which should perform best. This is the time-series equivalent of CV.