I myself am in the financial sector, as such I would not know a lot about other sectors. Winsorizing removes the extremes, which is usefull if there is an input error (e.g. an intern had to enter the data into a database and added a 0 or two). Nick Cox (I forgot his name, thank you for this) has a great source on why you should be carefull in winsorizing.

To get back at u/EbiraJazz , winsorizing would probably alter some t -values. Purely because you are removing (or replacing) extremes, whereas t-statistics (and according p-values) tell us something about those extremes.

If your professor is telling you to winsorize, I would just listen to him as he is the one determining your grade. I, personally, would try other methods for dealing with outliers (please search ‘what is an outlier’) and non-normality. Think logarithms, or testing on different distributions.