It will depend on what time you are going for them. If you are targeting them right now I'd use midges if the brook trout is located in a tiny trickle as those are the only bugs in those streams right now. Midges should work in general, fished tight-line style or under an indicator, whichever way you'd prefer, weighted or unweighted, though you'll need weight on the fly itself or added to the rig to get down to where the fish are, especially this time of the year when they are hugging bottom. I'd probably tight-line it on a small creek and use an indicator on a larger stream. Stealth will be key in winter unless the flows are up (which they probably are at this exact moment). With flows on the rise I'd probably second
@sandflyx and go with a weighted streamer such as a slumpbuster with a lot of lead in it. Black in terms of the color if it is murky and maybe attempt a white or chartreuse streamer if the water is a little stained. Jigging a streamer should be pretty effective. I am typically religiously opposed to running streamers. Not sure why that is. I mostly nymph.
I commend you on getting rid of the spinners. They have a higher impact on the fish in terms of unwanted damage caused by the hooks getting into parts of the fish you don't want them to and you will find a single barbless hook produces a fast release with the least amount of harm to come to to the fish. The thought of a native trout being caught an a treble is so horrific to me I can hardly even conjure it up inside my head.