There are a few lakes in the "area" that have trout in them. The closest one I can think of is Diamond Lake in Bayfield county. It's located between Lake Owen and Namekogan Lake. Another lake in the area is Atkins Lake, which is to the East of Diamond in the National Forest. Other lakes further north and west include Perch lake which is north of Drummond and Wanoka Lake just East of Ironriver. There may be more than that, but those are the ones I know offhand. Some of the aformentioned lakes have years where the fishing is closed for trout, make sure you reference the regulations before you go out. Good luck!
Trout regulations is a good place to start. Tells limits on lakes with trout. But now that I look at it only camp smith is shown. Round lake used to have planted browns, that was like 15 some years ago. Don't think they do that anymore. There's a couple lakes in Drummond that have stocked trout. Might have to go on the dnr website and look for lakes that they are stocking.
Are there any lakes in the Hayward area that you can ice fish for trout? I’ve can only find info on streams.