Not quite sure what wind would have to do with the draw on a fireplace? What happens to the millions of people that start up a fire when it is calm outside?
In any event, after making sure that your chimney is clear of any obstructions and having it professionally cleaned you neede to make sure that when you first start the fire the damper (if your fireplace has one) is completely open. In addition if your house has a tight seal you should open a nearby window a small amount so it can have a supply of fresh air.
Chimneys work on a simple principle - hot air goes up. If your house doesn't have a source of makeup air to replace the air going up the chimney then the makeup air comes DOWN the chimney (or other outlets like your furnace chimney). Any of these circumstances can cause death due to Carbon Monoxide poisoning since the exhaust gases are staying inside your house.
After the roaring blaze you have started calms down a bit you can close the window some so you don't let in to much cold air. And you might be able to close the damper a little so that it burns slower. If it is like my fireplace you need to leave the window and damper open to not get any smoke inside.