Yes Stubble there is a draw, but it is for anterless deer only.

Everyone can buy a buck tag (anything over 3" ) and then you enter a draw for anterless. Depending on where you hunt, the success rate for anterless varies from 10 - 100% chance of receiving one.

Some areas of Southern Ontario also have additional tags available as well.

This is for deer only. For moose, everyone draws a calf tag and you enter a draw for bulls/cows. The odds of getting one are based on the size of the group you enter into a pool. It' s almost impossible to get a tag all to yourself. The chances again range from 100% way north to almost 0% down near Sault Ste. Marie (the hub of the great lakes)