We have about 5 small garden beds, that we grow tomato, peppers, okra, egg plants etc. After the growing season (Apr - Sep; Toronto, Canada) we usually bury the left over stems and leave the beds exposed for the winter. I have read that covering up the beds with mulch would be better, keeping the soil warmer!. Is that so? What else should we do to prepare the garden for the winter?
It's a little late now, but planting cover crops is also a good idea. About the only thing you could plant right now (mid-October in Toronto) that would put on enough growth would be winter rye. Winter rye seed is cheap and easily available. The only real drawback is that it is hard to kill in the spring -- you'll need to hit it at least once with a heavy tiller.
Next year if you start earlier, you could plant oats, clover, fodder radish, or other cover crops. The benefit of some of these is that they reliably winter kill -- e.g. with oats you will essentially have a layer of straw on the beds in the spring. The trick is that you have to plant them early enough so that they can put on enough growth before hard freezes kill the plants. Late August is a good time to do this -- you can undersow in your main crops and then when you do your garden cleanup, don't uproot the main crop, just cut it off at the soil surface.
I would not recommend burying the debris in the garden. That could spread diseases. Pull all that and put it in a compost pile.
I don't mulch empty dirt. Sure, it gets cold. Then in May it gets warm. (I live about 90 minutes outside Toronto.)
We have just (Oct 21st) done a "final dig" on the garden, giving everything a thorough fluff-up and pulling up dead stuff to the compost. The exception is half a row of arugula and half a row of carrots that are still going strong. Sometime in the next week or two we will do one last thing: dig a trench about 4-6" deep for peas next year. Peas are happy to be planted when it's so cold and wet that digging a trench would hurt the soil. So we dig it now, and in the early spring just poke the peas into the dirt with a finger. Later we can fill in the trench to give the pea stems a little more support.
If you don't keep a garden diary, now is a good time to at least record what was planted where. Most things should not be planted in the same place every year.
I recommend Elliott Coleman's book "Four Season Harvest." He grows crops year 'round in Maine and provides a variety of techniques for preserving enough warmth to at least be eating greens in the dead of winter. His approaches are simple to complex with the simpler methods being the least expensive. I agree with the other reply, though: old stems and leaves from previous harvests should be removed from your growing area and composted. There is too much risk in spreading pathogens and disease without the warmth of the compost process to break down a garden's remnants. Adding compost to the cleared areas with give your garden a boost in the springtime.