The timeline should make the solution pretty clear, but to write it out explicitly:
In the morning, everyone goes out hunting. Sir Gilford wants Lord Barleyhew to give Sir Gilford's son William a plum political post (that Lord Barleyhew controls due to his rank in the Party). Sir Gilford pulls Lord Barleyhew aside and says "hey, unless you want me making certain information public, you'd better give William this post." And Lord Barleyhew says "what?!?!" and Sir Gilford says "come see me at my cabin after the hunting's over." What neither of them realizes is George Chickering overhears this and vows to follow up on it.
It starts to snow, and the hunting is called off. Sir Gilford says he's going out for a walk, but actually goes back to his cabin to await Lord Barleyhew, who eventually shows up. They have some argument, and Lord Barleyhew knuckles under after Sir Gilford shows him some incriminating information and the start of a letter he's written ("Gentlemen, I regret to inform you that things have come to my attention which cannot be overlooked." or somesuch). Lord Barleyhew leaves, and falling snow covers up both his and Sir Gilford's footsteps.
After it stops snowing, George Chickering comes in and demands to know what the deal is. Sir Gilford smirks, says he's got some hold on Lord Barleyhew, they argue, and Chickering bashes him on the head with the desk paperweight. Chickering freaks out, but decides he can try and make it look like suicide. He wipes off the paperweight with his handkerchief (which he throws in the fire), and puts Sir Gilford's revolver in the corpse's hand and makes it shoot itself in the head. He searches the desk and takes the folder of blackmail material (which he later mails to himself to get it out of the manor). He also takes the letter, rips away all but the first sentence, and leaves it in the hopes that it'll be taken for a suicide note. Chickering then puts on his improvised snowshoes (made out of grouse-beater paddles and fishing line) and walks out into the forest. Oh, and he switches shoes with the corpse, in the hopes that people will compare the corpse's shoes with the tracks in and assume they were made by Sir Gilford, so it'll look like Chickering was never there. This means he has to cram his feet into Sir Gilford's boots, probably ruining them, but oh well. When he gets back to his room he crams Sir Gilford's boots into the back of his dresser, hoping to later clean them and smuggle them back into Sir Gilford's room.
After lunch, William goes to see Sir Gilford. He does this because at the close of hunting, Sir Gilford told William to come see him after lunch (because Sir Gilford expected to have talked to Lord Barleyhew at this point and have successfully blackmailed him, and he wanted to tell William the deal, or at least hint at it). Charles Reed comes along to talk to John, the gamekeeper. William discovers Sir Gilford is dead and freaks out. He's worried that Sir Gilford's suicide will dishonor the family and ruin William's career, and maybe that people will think he himself killed Sir Gilford. William figures Edmund probably drove Sir Gilford to suicide, so why shouldn't he take the blame. William is fortunately carrying Edmund's watch (which Edmund lost the previous night, and the butler found and gave to William to return to Edmund, but William forgot), so he shoves it under the desk. William pockets the suicide note that Chickering left (since he wants it to look like murder), then writes a note purportedly from Sir Gilford telling Edmund to come to the cabin, then stages an argument with Sir Gilford so Charles Reed will hear and assume Sir Gilford is alive. Eventually William and Charles Reed walk back together, at which point William hands his note to the butler to give to Edmund.
Edmund gets the note and eventually walks to the cabin. On the doorstep, though, he decides that he doesn't want to get into another argument with his father, and turns and walks away into the woods, wandering around for a while before heading back to the manor. Sir Gilford's body lies there undiscovered until tea-time, at which point the game picks up.