I know you are probably all pumped and just wanting to plant steel and catch every coyote in your area. But you are picking probably the hardest animal and the worst weather conditions of the season to start.
My traps and gear of choice may differ from what the fellows are using in your part of the state. Which there are some that frequent this site. So I would imagine that they will respond and answer most if not all your question.
For 6 sets buy 6 #4 dukes.If its real thick area your going to be trapping I would buy 6 drags allso with atleast 8 foot of chain on them.The ground is froze hard so this will make it easier than trying to pound in cable stakes.I take it you don`t have any dry peatmoss or waxed dirt so take an axe and chop out a trap bed to place your trap in.Put a peace of wax paper their first then your trap and then cover with some grass or leaves.The wax paper will keep the trap from freezing down to the ground.With the ground being froze I would be makeing all flat sets or urine post sets.Use a skunky lure like gusto at a couple flat sets and just red fox or coyote urine at the urine post.Get out side and go kill something its better than watching TV.