I don't know how to trap without snow. I have 3 feet or so on most of my line now, will have close to 6 feet of settled snow by spring, more in the drifts.
I have Interior AK powder, so it may be nothing like the mush I've seen in the lower 48/coastal AK. I'm also below freezing - WAY below freezing - from a month or two before I set till mid-March.
First, forget everything you've ever heard about what fox and coyotes can and can't do, bedding traps, etc. Find a set of tracks and follow them - except for a couple days after a big dump, they get along just fine wherever they want to go (although they will stick to easy trails, especially if you provide one going about where they want to go anyway). You're not going to get a trap bedded solid in snow, and if you do it'll be the only solid thing out there. I usually set on a couple of small spruce branches, but I've been known to just huck a trap out and let it set where it lays.
Unless you have thawing temps, get rid of the wax paper. It's a pain to work with (but necessary if you're dealing with freeze/thaw). Paper towels work much better. They're easier to go on, look a lot like snow, hold a thin covering better, and don't wad up a big gob of snow that can prevent a trap from catching on like wax paper or plastic does. Wax paper or plastic under the trap will only make a nice iceblock - give the water somewhere to drain.
When you cover traps, don't disturb the snow - I use a big BBQ spatula - or it'll set up. With good fluffy powder, you can catch a fox with a trap under 6" or so of snow. Keep your covers thin - I seldom cover fox traps at all (but, from what I understand, the fox in AK are slightly suicidal). Coyote traps get maybe 1/4" cover.
RO's trick catches me a lot of fur. It works on snowshoes as well as a snogo. I generally set the trap right in my trail, but putting it off the trail should work if you have others in the area.
Go set some traps, and follow some tracks. Let the critters tell you what works and what doesn't.