Hi and welcome, CH24. Rick makes all the best arguments against using these rings above, but let me add my 2 cents worth. Down here in Florida, mulch is king and a lot of work and research goes into "what's the best mulch?".
Rubber and stones are almost worse than useless as mulch here in Florida (where everybody uses a LOT of mulch!). Both of them heat up in the sun, so fail to keep the soil cool for the plant, they don't hold together, so get scattered all over whenever somebody mows or weed-eats. Then in cold weather they don't insulate even half as well as an organic mulch.
For a brand-new very small tree, a mulch ring might cover enough of the roots to make a small difference when you need frost protection. Any tree that's been growing for at least 6 months i.e. if you planted a baby tree in the spring, can be assumed to have roots out beyond the spread of its branches. So most trees will outgrow the usefulness of a tree ring in a year or less.
But no tree ring is going to be thick enough or large enough to keep the soil warmer when the temps drop below freezing all night. Btw, you need to tell us where you live for us to judge what exactly will work for you. Please fill in your profile to include your location?
A 3in. to 4in. layer of wood chip mulch is going to do SO much more for your tree in terms of frost protection, plus soil moisture retention and weed prevention, it's not even worth thinking about. Go for the bagged wood chip mulch of your choice and use LOTS of it, spreading it a couple of feet beyond the width of the branches.
