I tend to leave as much standing as I can. Birds and other wildlife enjoy seeds, fruits, and protection from the elements that are left above the snow cover. I do remove anything know to be diseased. Quite a few things can be quite attractive in the winter garden.
Because most pests overwinter in the ground, I'm thinking about fluffing the soil of the entire garden down to about 3" this year, then spraying it too. Never done it before, but it's bound to be helpful.....
Sorry, but I'd have to differ on this one. I'd worry about killing anything beneficial in the soil. Also the overuse of pesticides can lead to strains of insects developing immunities to them, so when you really need them they don't work. It might be different if I knew I was combatting a known problem. (I also try not to till, especially in the autumn when there are lots of weed seeds around.)