You can totally can winter squash. You will need to pressure can them, and make sure they are cubed and not pureed.  

If you don’t want to pressure can them, you can also puree and freeze the squash. (If you go the freezing route, make sure you put the puree in straight-sided jars, because the contents can expand upwards during freezing).  

You can use your canned squash in many of the same recipes that you would use fresh squash in, but soups are one of the most popular and easy ways to use winter squash. 

Canning fun fact: while winter squash are totally can-able, summer squash cannot be canned because they contain too much moisture!  

Pressure Canning Winter Squash - Fillmore Container
Canning Butternut Squash - Healthy Canning

What to do with your preserved squash:
5 Ways to Use Canned Butternut Squash - The Kitchn
10 Best Canned Butternut Squash Recipes - Yummly
7 Recipes that Use Butternut Squash Puree - Treehugger