DingoBongo

I have a couple plants - not sure what species as they were gifted to me - that I planted late this summer. They're about 4 feet tall, and last week we got our first freeze. The person who gave them to me told me she cuts all hers down to soil level after the first freeze and mulches with pine straw. However, I've heard and read different advice. From what she said, to cutting with a few inches remaining above ground, to just leaving them alone to die off and then regrow in the spring.

So I'm wondering, what would happen if I didn't do anything? Is there any noticeable difference between cutting all the way vs. leaving a few inches? What about cutting but not mulching? Just curious if anyone knows the science behind these methods or the expected results of different approaches.