Do we have to split our dataset into training & testing when using ARIMA model?
Splitting in Train and Test sets or not depends from the purpose of your analysis. You can follow a statistical approach or a machine learning approach.

In the classical, statistical approach, you fit a model on the whole batch of data. Your goal here is to check the sign of the variables' parameters, and whether they are significant or not. Scientifically speaking, each of those parameters represents the test of an hypothesis.

In the machine learning approach, you want a model that is good at predicting data it has never seen before. You don't care whether a given variable has a positive or negative association with you dependend variable, you don't care whether your parameters are 95% significant or not, you just care that the model predicts the output as precisely as possible.

So, the answer to your question is: it depends! What do you need your model for?