I'm not certain but I think it may be a form of Juniper. Yes it's true that when these go brown they often don't recover but in your case I would not give up hope just yet. Some of the browning is on the branches which will naturally lignify and turn brown. There are also some brown shoots but you also have some new growth as well, so hang in there.
If my ID is even close, I would not bring this plant inside, leave it out. The soil appears to be in good condition and will probably require more frequent watering than you may be used to with other plants in conventional potting soil. Still, don't keep it constantly soggy either, allow it to dry down somewhat before you water again, always thoroughly BTW.
You still have some time to verify the ID before the weather gets too cold. Some protection will be required but for now don't worry. Can anyone else verify this or offer an alternative ID?