Yes, you can absolutely freeze Pillsbury cookie dough.
In fact, it may be recommended.
Freezing Pillsbury cookie dough allows you to hang on to it much longer, often at 2-3 months or more!
The way in which you choose to freeze cookie dough will depend on what types of Pillsbury dough you purchase.
While most Pillsbury cookie dough flavors will be fine frozen, whether or not the dough comes in a tube or ready to bake slices will influence your freezing method.