I haven't hunted the Powell area, but have hunted north of Gillette for about 3 years now. Powell & Gillette are about 4 hours apart. I hunt PD when I'm there and have seen some coyotes in the distance during the day. When I go in 2024 I do plan on shooting some coyotes as well this time around. I plan on hunting either just before dark or early morning. Where I go it's out in the middle of nowhere and you have to be very careful on the road due to wildlife.
If you shoot a few PD and put them in a bucket and dump them out in a pile where you're going to coyote hunt, it won't be too long when the smell starts getting out to them. PD may be far and few between in January, but they do come out on sunny days.
You can get maps from BLM that will help you plan your trip, I also use
BaseMaps.