Welcome to NGA,
@CH24 !
It would probably be helpful if we knew what planting zone you are in... are you talking about a "light frost" ? or a deep freeze such as we get in my area, in the Michigan Upper Peninsula? When it comes to tree roots, I don't think "frost" is too much of a problem (the top of the plant may suffer, however); and I also don't think a "mulch ring" is going to help much in terms of an actual freeze.
I believe the "mulch rings" are mainly intended for keeping the lawn around a tree tidy.
